fix: recycle Browser Run sessions on HTTP 410

[agent-think]

Closes #1980.

What changed

• treat Browser Run HTTP 410 Gone as a missing/expired session, alongside 404
• clear the stale shared-session record and transparently create a replacement
• retain errors for unrelated statuses such as 500
• add regression coverage for both the execution path and sessionInfo() cleanup
• add a patch changeset

Browser Run status validation

I deployed a temporary Browser Run probe and called the binding directly. It confirmed:

• GET /v1/devtools/browser/<expired-session>/json/list returns 410 with {"error":"Failed to list targets: 410"} after keep_alive expiry
• DELETE /v1/devtools/browser/<expired-session> returns 404 with {"error":"Failed to delete browser session: 404"}
• a never-created UUID returns 404 for both list and delete

This means connector liveness checks need to recognize both 404 (unknown/deleted) and 410 (expired), while continuing to surface all other errors.

Verification

• regression proof: the new HTTP 410 recycling test fails against the old helper (after all 3 configured retries) with BrowserRenderingError ... status: 410
• pnpm --filter agents exec vitest run --config src/tests/vitest.config.ts src/tests/browser-connector.test.ts — 34 passed
• pnpm run check — passed (all 117 TypeScript projects)
• pnpm run build — passed (25 projects)
• packed the changed agents build and deployed a temporary full-stack Browser Run demo; its API returned passed: true with a new replacement session ID after the injected stale-session 410

Demo: https://issue-1980-browser-session-recycle.magnificent-supermarket.workers.dev

---

[changeset-bot]

🦋 Changeset detected

Latest commit: f778708

The changes in this PR will be included in the next version bump.

This PR includes changesets to release 2 packages

Name	Type
agents	Patch
@cloudflare/agent-think	Patch

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[devin-ai-integration]

✅ Devin Review: No Issues Found

Devin Review analyzed this PR and found no bugs or issues to report.

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commit: f778708