[BUG] Claude in Chrome: tabGroupId flaps between tabs_context_mcp calls; actions on just-listed tabs fail with "Couldn't determine which page this action targets"

Preflight Checklist

• [x] I have searched existing issues and this hasn't been reported yet
• [x] This is a single bug report
• [x] I am using the latest version of Claude Code

What's Wrong?

Claude Code: 2.1.247 (CLI)
OS: macOS (Darwin 25.6.0)
Browser: Google Chrome, Claude in Chrome extension connected

While automating a docs.google.com form fill from the CLI, the extension's tab tracking became inconsistent mid-session and stayed that way:

1. tabs_context_mcp returned a different tabGroupId on consecutive calls with no user tab changes: 1734025282 → 1131221108 → 1133103867 → back to 1131221108. The tab listed inside the group changed accordingly (same underlying form page, different tabId).
2. navigate to the Google Forms URL succeeded (get_page_text returned the full form, read_page returned element refs).
3. Subsequent form_input / read_page / browser_batch calls on the same tabId that tabs_context_mcp had just listed failed with either Tab <id> no longer exists. Call tabs_context_mcp to get current tabs. or, persistently, Couldn't determine which page this action targets. Re-read tabs_context_mcp and try again.
4. Re-reading tabs_context_mcp immediately before retrying made no difference — the tab appears in the context result, and the very next action on it fails.
5. Inconsistency within the same window: tabs_create_mcp succeeded and returned a new tabId while read_page on the listed, loaded tab failed.
6. One browser_batch (navigate + wait + read_page) timed out with "The Chrome extension is connected but the page may be loading, unresponsive, or waiting on a permission prompt in the extension side panel" — but no site-approval prompt was visible to surface, so if one was pending it was never shown. Possibly adjacent to the (closed) #85999, though that case was hard permission denials on every domain; here actions intermittently succeed and the distinctive symptom is the tab-group identity flapping.

Expected

Actions target the tab that tabs_context_mcp just returned; the tab group id is stable across calls within one session; if a site-approval prompt is blocking actions, the error says so explicitly (or the prompt is surfaced).

Repro (as observed)

1. From Claude Code CLI, tabs_context_mcp {createIfEmpty:true} → note tabGroupId.
2. navigate a listed tab to a docs.google.com/forms/... URL; read_page (works, refs returned).
3. Call form_input on a returned ref → "Tab no longer exists".
4. tabs_context_mcp again → different tabGroupId, form tab listed under a new/old tabId.
5. Any action on that listed tabId → "Couldn't determine which page this action targets", repeatably.

Timestamps: 2026-08-27, tabIds observed: 127118507, 127117940, 127117943.