feat(loops): Make builder sessions resumable from the loops page

[charlesvien]

Problem

Starting the loop builder from the loops page creates an anonymous repo-less cloud task and navigates to it. Leaving that task (clicking another task, going back to Loops) left no way back: the loops page had no memory of the session and the sidebar row was titled with the raw prompt, indistinguishable from any other task.

Changes

• Builder tasks are now titled "Loop builder: " so the sidebar row is recognizable. The chat content still gets the raw prompt.
• Each started builder session is recorded in a persisted per-device store and shown as a "Builder in progress" row above the composer on the loops page, with a Resume button back to the task.
• Rows only show while the cloud run is actually alive: task summaries are polled and sessions whose sandbox shut down (completed, failed, cancelled, archived or deleted task) are pruned automatically.
• Each row has a Stop button that ends the run through the same stopCloudRun path as the task view's "Stop run" button, then removes the row.
• useInboxCloudTaskRunner gained an onTaskCreated callback so variants can observe the created task.

How did you test this?

• New unit tests for the session store (ordering, dedupe, cap, removal); ran the loops, inbox and scouts vitest suites.
• pnpm --filter @posthog/ui typecheck and Biome on the touched files.

Automatic notifications

• Publish to changelog?
• Alert Sales and Marketing teams?

[github-actions]

React Doctor found no issues in the changed files. 🎉

_{Reviewed by React Doctor for commit 1d5c806.}

[trunk-io]

😎 This pull request was merged.

[posthog]

✅ Visual changes approved by @charlesvien — baseline updated in 035e9f5.

View this run in PostHog

2 changed.

[veria-ai]

PR overview

All previously flagged issues have been addressed. No open security concerns remain on this pull request.

Security review

No open security issues remain on this pull request.

Fixed/addressed: 1 · PR risk: 0/10

[greptile-apps]

_{Reviews (1): Last reviewed commit: "make loop builder sessions resumable" | Re-trigger Greptile}

[github-actions]

Contained UI feature (resumable loop-builder sessions) with real test coverage; the one substantive review concern (cross-account prompt persistence) is verifiably fixed in the diff via identity-scoped storage and a version migration that drops unattributed legacy entries, corroborated by a bot follow-up comment. No risky-territory surface (auth, billing, migrations, CI, deps) is touched.

• Author wrote 67% of the modified lines and has 155 merged PRs in these paths (familiarity MODERATE).
• 👍 on the PR from greptile-apps[bot].

Gate mechanics and policy version

Gate		Result
prerequisites	✓	all clear
deny-list	✓	no deny categories matched
size	✓	347L, 8F substantive, 538L/10F incl. docs/generated/snapshots — within ceiling
tier	✓	T1-agent / T1d-complex (538L, 10F, two-areas, feat)
stamphog 2.0.0b3		.stamphog/policy.yml @ 0092213 · reviewed head d583d63

New commits pushed (delta classified non_trivial_delta) — stamphog approval dismissed; re-review running automatically.

[github-actions]

Contained UI feature (loop builder resumability) with no auth/billing/crypto/API/dependency/CI/migration surface touched; the one substantive security concern (cross-account prompt leakage) was verifiably fixed in the diff via per-identity scoping and a version-bump migration that drops unattributed entries, and an agent reviewer confirmed no open concerns remain.

• Author wrote 67% of the modified lines and has 155 merged PRs in these paths (familiarity MODERATE).
• 👍 on the PR from greptile-apps[bot].

Gate mechanics and policy version

Gate		Result
prerequisites	✓	all clear
deny-list	✓	no deny categories matched
size	✓	347L, 8F substantive, 538L/10F incl. docs/generated/snapshots — within ceiling
tier	✓	T1-agent / T1d-complex (538L, 10F, two-areas, feat)
stamphog 2.0.0b3		.stamphog/policy.yml @ 0092213 · reviewed head 035e9f5

New commits pushed (delta classified non_trivial_delta) — stamphog approval dismissed; re-review running automatically.

[github-actions]

Contained client-side UI/feature work (loop builder session tracking) with no touch on auth, billing, migrations, dependencies, or CI; the one security concern a bot reviewer raised (cross-account prompt leakage) is verifiably fixed in the diff via per-identity scoping and a store migration that drops unattributed entries, and it's covered by new unit tests.

• Author wrote 80% of the modified lines and has 155 merged PRs in these paths (familiarity STRONG).
• 👍 on the PR from greptile-apps[bot].

Gate mechanics and policy version

Gate		Result
prerequisites	✓	all clear
deny-list	✓	no deny categories matched
size	✓	347L, 9F substantive, 538L/11F incl. docs/generated/snapshots — within ceiling
tier	✓	T1-agent / T1d-complex (538L, 11F, two-areas, feat)
stamphog 2.0.0b3		.stamphog/policy.yml @ 0092213 · reviewed head a8ff0f7

New commits pushed (delta classified non_trivial_delta) — stamphog approval dismissed; re-review running automatically.

[github-actions]

Local-only UI feature (builder session resumability on the loops page) with no changes to APIs, data models, auth flows, billing, or dependencies; the one flagged privacy concern (persisted sessions leaking across accounts) is visibly fixed in this diff via per-identity scoping and a store version bump that drops unattributed legacy entries, and new unit tests cover the store and liveness logic.

• Author wrote 21% of the modified lines and has 169 merged PRs in these paths (familiarity MODERATE).
• 👍 on the PR from greptile-apps[bot].

Gate mechanics and policy version

Gate		Result
prerequisites	✓	all clear
deny-list	✓	no deny categories matched
size	✓	381L, 16F substantive, 572L/18F incl. docs/generated/snapshots — within ceiling
tier	✓	T1-agent / T1d-complex (572L, 18F, two-areas, feat)
stamphog 2.0.0b3		.stamphog/policy.yml @ 0092213 · reviewed head 1d5c806