feat: add chat read/unread indicator to sidebar (#23129)

## Summary

Adds read/unread tracking for chats so users can see which agent
conversations have new assistant messages they haven't viewed.

## Backend Changes

- Adds `last_read_message_id` column to the `chats` table (migration
000439).
- Computes `has_unread` as a virtual column in `GetChatsByOwnerID` using
an `EXISTS` subquery checking for assistant messages beyond the read
cursor.
- Exposes `has_unread` on the `codersdk.Chat` struct and auto-generated
TypeScript types.
- Updates `last_read_message_id` on stream connect/disconnect in
`streamChat`, avoiding per-message API calls during active streaming.
- Uses `context.WithoutCancel` for the deferred disconnect write so the
DB update succeeds even after the client disconnects.

## Frontend Changes

- Bold title (`font-semibold`) for unread chats in the sidebar.
- Small blue dot indicator next to the relative timestamp.
- Suppresses unread indicator for the currently active chat via
`isActive` from NavLink.

## Design Decisions

- Only `assistant` messages count as unread — the user's own messages
don't trigger the indicator.
- No foreign key on `last_read_message_id` since messages can be deleted
(via rollback/truncation) and the column is just a high-water mark.
- Zero API calls during streaming: exactly 2 DB writes per stream
session (connect + disconnect).
- Unread state refreshes on chat list load and window focus. The
`watchChats` WebSocket optimistically marks non-active chats as unread
on `status_change` events, but does not carry a server-computed
`has_unread` field. Navigating to a chat optimistically clears its
unread indicator in the cache.

coderd/database/db2sdk/db2sdk.go

@@ -1575,23 +1575,24 @@ func Chat(c database.Chat, diffStatus *database.ChatDiffStatus) codersdk.Chat {
 	return chat
 }
 
-// Chats converts a slice of database.Chat to codersdk.Chat, looking
-// up diff statuses from the provided map. When diffStatusesByChatID
-// is non-nil, chats without an entry receive an empty DiffStatus.
-func Chats(chats []database.Chat, diffStatusesByChatID map[uuid.UUID]database.ChatDiffStatus) []codersdk.Chat {
-	result := make([]codersdk.Chat, len(chats))
-	for i, c := range chats {
-		diffStatus, ok := diffStatusesByChatID[c.ID]
+// ChatRows converts a slice of database.GetChatsRow (which embeds
+// Chat plus HasUnread) to codersdk.Chat, looking up diff statuses
+// from the provided map. When diffStatusesByChatID is non-nil,
+// chats without an entry receive an empty DiffStatus.
+func ChatRows(rows []database.GetChatsRow, diffStatusesByChatID map[uuid.UUID]database.ChatDiffStatus) []codersdk.Chat {
+	result := make([]codersdk.Chat, len(rows))
+	for i, row := range rows {
+		diffStatus, ok := diffStatusesByChatID[row.Chat.ID]
 		if ok {
-			result[i] = Chat(c, &diffStatus)
-			continue
-		}
-
-		result[i] = Chat(c, nil)
-		if diffStatusesByChatID != nil {
-			emptyDiffStatus := ChatDiffStatus(c.ID, nil)
-			result[i].DiffStatus = &emptyDiffStatus
+			result[i] = Chat(row.Chat, &diffStatus)
+		} else {
+			result[i] = Chat(row.Chat, nil)
+			if diffStatusesByChatID != nil {
+				emptyDiffStatus := ChatDiffStatus(row.Chat.ID, nil)
+				result[i].DiffStatus = &emptyDiffStatus
+			}
 		}
+		result[i].HasUnread = row.HasUnread
 	}
 	return result
 }

coderd/database/db2sdk/db2sdk_test.go

@@ -554,8 +554,15 @@ func TestChat_AllFieldsPopulated(t *testing.T) {
 
 	v := reflect.ValueOf(got)
 	typ := v.Type()
+	// HasUnread is populated by ChatRows (which joins the
+	// read-cursor query), not by Chat, so it is expected
+	// to remain zero here.
+	skip := map[string]bool{"HasUnread": true}
 	for i := range typ.NumField() {
 		field := typ.Field(i)
+		if skip[field.Name] {
+			continue
+		}
 		require.False(t, v.Field(i).IsZero(),
 			"codersdk.Chat field %q is zero-valued — db2sdk.Chat may not be populating it",
 			field.Name,