fix(stream): chat insert 400 — insert body must declare snippet.type

The liveChatId fix (TASK 44) worked on the next Test Stream, but every Mock
Chat Input send returned 'YouTube rejected the message (error 400)'. The
runtime log's body: 400 MISSING_REQUIRED_FIELD, domain
youtube.api.v3.LiveChatMessageInsertResponse.Error.

The liveChat/messages.insert snippet requires type ('textMessageEvent' or
'pollEvent') alongside liveChatId and textMessageDetails.messageText; the
TASK 41 body omitted it, and the Good Dog test asserted only liveChatId +
messageText were present — false-green while real YouTube rejected every
send. Fix body + assert type in the same test so the field can never drop
silently again.

Reference: https://developers.google.com/youtube/v3/live/docs/liveChatMessages/insert

Good Dog: ONE integration test (strengthened TestStream_DockTooling...).
Gate: clean build 0 warnings; full vstest 317/318 (the 1 failure is the
known environmental RealMouseDrag flake — passes 3/3 in isolation).

TASKS.md

@@ -60,6 +60,7 @@
 | 42 | Top bar redesign: one REC-or-Stream surface, gear up top, sign-in/account zone world-gated | ✅ Done (2026-09-22) | [`TASKS/task-42-top-bar-redesign.md`](TASKS/task-42-top-bar-redesign.md) |
 | 43 | Native events & alerts: chat parity (all six event types + server poll cadence) + six-animation native alert box | ✅ Done (2026-09-24) | [`TASKS/task-43-native-alerts.md`](TASKS/task-43-native-alerts.md) |
 | 44 | TEST-tab chat fix: resolve liveChatId from snippet (not contentDetails) + poll until the broadcast is live | ✅ Done (2026-09-25); full suite 318/318 | [`TASKS/task-44-test-chat-fix.md`](TASKS/task-44-test-chat-fix.md) |
+| 45 | TEST-tab chat fix #2: insert body must declare `snippet.type` (400 MISSING_REQUIRED_FIELD) | ✅ Done (2026-09-25) | [`TASKS/task-45-chat-insert-type.md`](TASKS/task-45-chat-insert-type.md) |
 
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