Fill on `<input type="date">` and `<input type="time">` confirmed not working

**Before submitting an issue, please:**

- [x] Check the documentation: https://docs.stagehand.dev/
- [x] Search existing issues: https://github.com/browserbase/stagehand/issues

## Environment Information

**Stagehand:**

- Language/SDK: TypeScript
- Stagehand version: 3.0.1
- Chrome: 144

## Issue Description

Locator.fill() (and act({ method: 'fill' })) on native HTML5 date/time inputs resolve without error, but an immediate locator.inputValue() reads back an empty string. Setting the value via the native setter inside the page context (evaluate) and dispatching input/change events succeeds consistently.

### Steps to Reproduce

1. Initialize Stagehand locally (no LLM needed).
2. Navigate to a data: URL containing a native `<input type="date">` (and optionally `<input type="time">`).
3. Call `page.locator(xpath).fill('2025-11-15')`; immediately call `locator.inputValue()` — observe empty string.
4. Call `stagehand.act({ selector, method: 'fill', arguments: [...] })`; immediately call `locator.inputValue()` — observe empty string.
5. Call `page.evaluate()` to set via native setter and dispatch input/change; immediately call `locator.inputValue()` — observe the expected value.

### Minimal Reproduction Code

<img width="1288" height="354" alt="Image" src="https://github.com/user-attachments/assets/3248b86e-d607-4e51-80f4-410968f6afe3" />

````ts
import { Stagehand } from "@browserbasehq/stagehand";

function htmlDemo() {
return `<!doctype html>

  <meta charset="utf-8" />
  <title>Stagehand date/time fill demo</title>
  <style>
    body { font-family: system-ui, sans-serif; margin: 24px; }
    .grid { display: grid; grid-template-columns: repeat(3, 1fr); gap: 16px; }
    .card { border: 1px solid #ddd; border-radius: 8px; padding: 16px; }
    .card h2 { margin: 0 0 8px; font-size: 16px; }
    .row { margin: 8px 0; display: flex; gap: 8px; align-items: center; }
    label { display: inline-flex; align-items: center; gap: 6px; }
    input { padding: 6px 8px; border: 1px solid #ccc; border-radius: 6px; }
    .status { margin-top: 8px; font-size: 12px; color: #555; }
    .ok input { border-color: #16a34a; box-shadow: 0 0 0 2px #16a34a22; }
    .ok .status { color: #16a34a; }
    .fail input { border-color: #dc2626; box-shadow: 0 0 0 2px #dc262622; }
    .fail .status { color: #dc2626; }
    .hint { color: #666; font-size: 12px; margin-bottom: 8px; }
  </style>
  <h1>Stagehand native date/time fill — broken vs working</h1>
  <p class="hint">Demonstrates two broken approaches (locator.fill, act(fill)) and one working approach (evaluate with native setter).</p>
  <div class="grid">
    <div class="card" id="card-loc">
      <h2>Locator.fill()</h2>
      <div class="row"><label>Date <input id="d_loc" type="date"></label></div>
      <div class="row"><label>Time <input id="t_loc" type="time"></label></div>
      <div class="status" id="status_loc">Pending…</div>
    </div>
    <div class="card" id="card-act">
      <h2>act({ method: 'fill' })</h2>
      <div class="row"><label>Date <input id="d_act" type="date"></label></div>
      <div class="row"><label>Time <input id="t_act" type="time"></label></div>
      <div class="status" id="status_act">Pending…</div>
    </div>
    <div class="card" id="card-eval">
      <h2>Evaluate (native setter)</h2>
      <div class="row"><label>Date <input id="d_eval" type="date"></label></div>
      <div class="row"><label>Time <input id="t_eval" type="time"></label></div>
      <div class="status" id="status_eval">Pending…</div>
    </div>
  </div>`;
}

async function setViaEvaluate(page: any, selector: string, val: string) {
await page.evaluate(({ xp, val }) => {
const doc = (globalThis as any).document;
const xpExpr = xp.startsWith("xpath=") ? xp.slice(6) : xp;
const res = doc.evaluate(xpExpr, doc, null, 9, null);
const el = res.singleNodeValue as any;
if (!el || String(el.tagName || "").toUpperCase() !== "INPUT") return;
const desc = (globalThis as any).HTMLInputElement?.prototype &&
Object.getOwnPropertyDescriptor((globalThis as any).HTMLInputElement.prototype, "value");
if (desc && typeof desc.set === "function") desc.set.call(el, val);
else el.value = String(val);
const E = (globalThis as any).Event;
el.dispatchEvent(new E("input", { bubbles: true }));
el.dispatchEvent(new E("change", { bubbles: true }));
}, { xp: selector, val });
}

async function markCard(page: any, cardId: string, dateId: string, timeId: string, readDate: string, readTime: string, expectDate: string, expectTime: string) {
await page.evaluate(({ cardId, dateId, timeId, readDate, readTime, expectDate, expectTime }) => {
const doc = (globalThis as any).document;
const card = doc.getElementById(cardId);
const d = doc.getElementById(dateId) as any;
const t = doc.getElementById(timeId) as any;
const status = doc.getElementById('status\_' + cardId.split('-')[1]);
const ok = readDate === expectDate && readTime === expectTime;
if (card) card.classList.remove('ok','fail');
if (card) card.classList.add(ok ? 'ok' : 'fail');
if (status) status.textContent = `Date=${JSON.stringify(readDate)} Time=${JSON.stringify(readTime)} ${ok ? '✓ OK' : '✗ FAIL'}`;
// Also reflect final values in the inputs for visibility
if (d) d.value = readDate;
if (t) t.value = readTime;
}, { cardId, dateId, timeId, readDate, readTime, expectDate, expectTime });
}

async function main() {
const sh = new Stagehand({ env: "LOCAL", verbose: 1, localBrowserLaunchOptions: { headless: false } });
await sh.init();
const page = sh.context.pages()[0];
if (!page) throw new Error("no page");

await page.goto(`data:text/html,${encodeURIComponent(htmlDemo())}`);
await page.waitForLoadState("domcontentloaded");

const date = "2025-11-15";
const time = "10:00";

// Locator.fill() card
await page.locator('xpath=//_[@id="d_loc"]').fill(date);
await page.locator('xpath=//_[@id="t_loc"]').fill(time);
const dLoc = await page.locator('xpath=//_[@id="d_loc"]').inputValue();
const tLoc = await page.locator('xpath=//_[@id="t_loc"]').inputValue();
await markCard(page, 'card-loc', 'd_loc', 't_loc', dLoc, tLoc, date, time);

// act({ method: 'fill' }) card
await sh.act({ selector: 'xpath=//_[@id="d_act"]', description: 'date via act', method: 'fill', arguments: [date] });
await sh.act({ selector: 'xpath=//_[@id="t_act"]', description: 'time via act', method: 'fill', arguments: [time] });
const dAct = await page.locator('xpath=//_[@id="d_act"]').inputValue();
const tAct = await page.locator('xpath=//_[@id="t_act"]').inputValue();
await markCard(page, 'card-act', 'd_act', 't_act', dAct, tAct, date, time);

// Evaluate (native setter) card
await setViaEvaluate(page, 'xpath=//_[@id="d_eval"]', date);
await setViaEvaluate(page, 'xpath=//_[@id="t_eval"]', time);
const dEval = await page.locator('xpath=//_[@id="d_eval"]').inputValue();
const tEval = await page.locator('xpath=//_[@id="t_eval"]').inputValue();
await markCard(page, 'card-eval', 'd_eval', 't_eval', dEval, tEval, date, time);

console.log("\nOpen browser to see three cards: two broken (red), one working (green). Close tab to finish.");
}

main().catch((err) => { console.error(err); process.exit(1); });

````

### Error Messages / Log trace

```

============================================================
BROKEN PATHS (expected to be flaky or empty)
============================================================
Date: locator.fill → inputValue (expected empty)

[2025-11-08T06:25:12.978Z] DEBUG: xpath main-world
    frameId: 55A9F6AEBE837C4D00A34C645D4510D3
    xp: //*[@id="d"]
    ctxId: 2
[2025-11-08T06:25:12.984Z] DEBUG: xpath main-world
    frameId: 55A9F6AEBE837C4D00A34C645D4510D3
    xp: //*[@id="d"]
    ctxId: 2
[2025-11-08T06:25:12.998Z] DEBUG: xpath main-world
    frameId: 55A9F6AEBE837C4D00A34C645D4510D3
    xp: //*[@id="d"]
    ctxId: 2
after fill: ""

Date: act(fill) → inputValue (expected empty)

[2025-11-08T06:25:13.025Z] DEBUG: xpath main-world
    frameId: 55A9F6AEBE837C4D00A34C645D4510D3
    xp: //*[@id="d"]
    ctxId: 2
after act(fill): ""

Time: locator.fill → inputValue (expected empty)

[2025-11-08T06:25:13.028Z] DEBUG: xpath main-world
    frameId: 55A9F6AEBE837C4D00A34C645D4510D3
    xp: //*[@id="t"]
    ctxId: 2
[2025-11-08T06:25:13.031Z] DEBUG: xpath main-world
    frameId: 55A9F6AEBE837C4D00A34C645D4510D3
    xp: //*[@id="t"]
    ctxId: 2
[2025-11-08T06:25:13.035Z] DEBUG: xpath main-world
    frameId: 55A9F6AEBE837C4D00A34C645D4510D3
    xp: //*[@id="t"]
    ctxId: 2
after fill: ""

Time: act(fill) → inputValue (expected empty)

[2025-11-08T06:25:13.058Z] DEBUG: xpath main-world
    frameId: 55A9F6AEBE837C4D00A34C645D4510D3
    xp: //*[@id="t"]
    ctxId: 2
after act(fill): ""

============================================================
WORKING PATHS (expected to succeed)
============================================================
Date: evaluate(native setter) → inputValue (expected "2025-11-15")

[2025-11-08T06:25:13.063Z] DEBUG: xpath main-world
    frameId: 55A9F6AEBE837C4D00A34C645D4510D3
    xp: //*[@id="d"]
    ctxId: 2
after evaluate: "2025-11-15"

Time: evaluate(native setter) → inputValue (expected "10:00")

[2025-11-08T06:25:13.068Z] DEBUG: xpath main-world
    frameId: 55A9F6AEBE837C4D00A34C645D4510D3
    xp: //*[@id="t"]
    ctxId: 2
after evaluate: "10:00"

Done. Close the browser to finish.

```

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Fill on `<input type="date">` and `<input type="time">` confirmed not working #1249

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Fill on <input type="date"> and <input type="time"> confirmed not working #1249

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Fill on `<input type="date">` and `<input type="time">` confirmed not working #1249