fix(chat): clear stale thinking runs reliably

[Niko96-dotcom]

Summary

• Snapshot the chat message list once when a response wait starts, so a completed assistant message can clear the Thinking indicator instead of moving the baseline forward.
• Treat persisted complete run statuses as terminal in the active-run polling fallback.
• Serialize persisted run updates per run and write through a temp file + rename to avoid lost updates or malformed JSON from concurrent writes.

Tests

• pnpm test src/screens/chat/chat-screen-utils.test.ts src/server/run-store.test.ts
• pnpm build

Note: I also ran the full pnpm test locally; it currently fails in unrelated existing suites on current main (MCP hub search expectations, gateway env resolution, i18n label text, context usage helper export, composer/context copy checks, chat-message-list helpers, and playground localStorage setup). This patch-specific coverage passes.

[outsourc-e]

Closing as superseded by #432. The validated fix was folded into the consolidated batch branch fix/issue-sweep-batch-20260514 for one review/merge path.