fix(chat): Improve content/input overlap

* Avoid overlap as much as possible
* Fix scroll bar positioning
* When input is floating, we add a `shadow` class

Fixes #1855

Author: gadenbuie

js/chat/chat.scss

@@ -3,13 +3,14 @@ shiny-chat-container {
   --shiny-chat-user-message-bg: RGBA(var(--bs-primary-rgb, 0, 123, 194), 0.06);
   --_chat-container-padding: 0.25rem;
 
-  display: flex;
-  flex-direction: column;
+  display: grid;
+  grid-template-columns: 1fr;
+  grid-template-rows: 1fr auto;
   margin: 0 auto;
-  gap: 1rem;
-  overflow: auto;
+  gap: 0.625rem;
   padding: var(--_chat-container-padding);
   padding-bottom: 0; // Bottom padding is on input element
+  overflow: clip;
 
   p:last-child {
     margin-bottom: 0;
@@ -54,6 +55,12 @@ shiny-chat-messages {
   display: flex;
   flex-direction: column;
   gap: 2rem;
+  overflow: auto;
+
+  // Make space for the scroll bar
+  --_scroll-margin: 1rem;
+  padding-right: var(--_scroll-margin);
+  margin-right: calc(-1 * var(--_scroll-margin));
 }
 
 shiny-chat-message {
@@ -96,13 +103,12 @@ shiny-chat-message {
 }
 
 shiny-chat-input {
-  --_input-padding-top: 1rem;
+  --_input-padding-top: 0;
   --_input-padding-bottom: var(--_chat-container-padding, 0.25rem);
 
-  margin-top: auto;
+  margin-top: calc(-1 * var(--_input-padding-top));
   position: sticky;
-  bottom: 0;
-  background: linear-gradient(to bottom, transparent, var(--bs-body-bg, white) calc(var(--_input-padding-top) - var(--_input-padding-bottom)));
+  bottom: calc(-1 * var(--_input-padding-bottom));
   padding-block: var(--_input-padding-top) var(--_input-padding-bottom);
 
   textarea {
@@ -133,6 +139,12 @@ shiny-chat-input {
   }
 }
 
+shiny-chat-input-sentinel {
+  // sentinel element with 0 height that lets us know when input element is floating
+  height: 0;
+  width: 100%;
+}
+
 /*
   Disable the page-level pulse when the chat input is disabled
   (i.e., when a response is being generated and brought into the chat)

js/chat/chat.ts

@@ -46,6 +46,7 @@ const CHAT_MESSAGE_TAG = "shiny-chat-message";
 const CHAT_USER_MESSAGE_TAG = "shiny-user-message";
 const CHAT_MESSAGES_TAG = "shiny-chat-messages";
 const CHAT_INPUT_TAG = "shiny-chat-input";
+const CHAT_INPUT_SENTINEL_TAG = "shiny-chat-input-sentinel";
 const CHAT_CONTAINER_TAG = "shiny-chat-container";
 
 const ICONS = {
@@ -262,6 +263,8 @@ class ChatInput extends LightElement {
 }
 
 class ChatContainer extends LightElement {
+  inputSentinel?: HTMLElement;
+  inputSentinelObserver?: IntersectionObserver;
 
   private get input(): ChatInput {
     return this.querySelector(CHAT_INPUT_TAG) as ChatInput;
@@ -280,6 +283,34 @@ class ChatContainer extends LightElement {
     return html``;
   }
 
+  connectedCallback(): void {
+    super.connectedCallback();
+
+    // We use a sentinel element that we place just above the shiny-chat-input. When it
+    // moves off-screen we know that the text area input is now floating, add shadow.
+    let sentinel = this.querySelector<HTMLElement>(CHAT_INPUT_SENTINEL_TAG);
+    if (!sentinel) {
+      sentinel = createElement(CHAT_INPUT_SENTINEL_TAG, {}) as HTMLElement;
+      this.input.insertAdjacentElement("beforebegin", sentinel);
+    }
+
+    this.inputSentinel = sentinel;
+    this.inputSentinelObserver = new IntersectionObserver(
+      (entries) => {
+        const inputTextarea = this.input.querySelector("textarea");
+        if (!inputTextarea) return;
+        const addShadow = entries[0]?.intersectionRatio === 0;
+        inputTextarea.classList.toggle("shadow", addShadow);
+      },
+      {
+        threshold: [0, 1],
+        rootMargin: "0px",
+      }
+    );
+
+    this.inputSentinelObserver.observe(this.inputSentinel);
+  }
+
   firstUpdated(): void {
     // Don't attach event listeners until child elements are rendered
     if (!this.messages) return;
@@ -306,6 +337,9 @@ class ChatContainer extends LightElement {
   disconnectedCallback(): void {
     super.disconnectedCallback();
 
+    this.inputSentinelObserver?.disconnect();
+    this.inputSentinel?.remove();
+
     this.removeEventListener("shiny-chat-input-sent", this.#onInputSent);
     this.removeEventListener("shiny-chat-append-message", this.#onAppend);
     this.removeEventListener(