[browser rendering] Update stagehand snippet to Zod 4

[vicb]

Existing documentation URL(s)

cloudflare/workers-sdk#10798

What changes are you suggesting?

The worker code relies on Zod v3, however Zod v4 has been released.

I have added a note about zod requirements in this PR

There is 2 things we should do:

• Add a package.json with pinned version so that users copy/pasting the code get a working sample
• Probably update to Zod v4

Additional information

@kathayl it looks like you created this page, could you please help address this issue?

[garysassano]

Implementation Notes

• Compatibility: Stagehand added Zod 4 support in v2.4.3
• JSON Schema: Zod 4 includes native JSON Schema support, eliminating the need for the zod-to-json-schema package in workerAIClient.ts

[garysassano]

Apparently, Stagehand still doesn't provide actual support for Zod 4:

• Using Zod 4 results in cryptic TypeError during runtime browserbase/stagehand#938
• Zod 4 compatibility issue with latest version׳s agent api browserbase/stagehand#1029
• Problems with ZodV4 dependent project trying to use Stagehand browserbase/stagehand#1098

Stagehand is still only compatible for zod v3 but for convenience we allow users to have zod 4 installed. To use zod v3 in Stagehand, you just have to import from zod v3.

import { z } from "zod/v3";