feat(loops): Add analytics events for loops

[charlesvien]

Problem

Loops has no product analytics beyond the three promo-card events, so we cannot see adoption, configuration choices or run engagement for the feature at all.

Changes

Adds a typed loops event family to packages/shared/src/analytics-events.ts and wires track(...) calls in the loops UI:

• Loop list viewed and Loop viewed for the list and detail surfaces
• Loop created, Loop updated and Loop deleted for the lifecycle
• Loop enabled toggled for pause/resume, with was_auto_paused to separate clearing a billing or failure auto-pause from a routine toggle
• Loop run started, Loop run blocked (with the backend block reason) and Loop run viewed for the manual-run funnel

Names and property shapes follow the existing conventions in that file: sentence-case names, snake_case properties and EventPropertyMap entries. Properties carry only ids, enums, booleans and counts, never loop names or prompt text. No visual changes, so no screenshots.

How did you test this?

• pnpm --filter @posthog/shared typecheck and pnpm --filter @posthog/ui typecheck
• biome check on the changed files
• vitest run loops in packages/ui (6 files, 113 tests, all passing)

Automatic notifications

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

[trunk-io]

😎 This pull request was merged.

[github-actions]

React Doctor found no issues in the changed files. 🎉

_{Reviewed by React Doctor for commit 9ab43cf.}

[greptile-apps]

Prompt To Fix All With AI

Fix the following 1 code review issue. Work through them one at a time, proposing concise fixes.

---

### Issue 1 of 1
packages/ui/src/features/loops/components/LoopsListView.tsx:105-106
**Builder-session count freezes early**

When persisted builder sessions exist while their task summaries are still loading, this effect permanently records the pre-liveness-check count, causing `builder_session_count` to include sessions that are subsequently removed as ended.

_{Reviews (1): Last reviewed commit: "add loops analytics events" | Re-trigger Greptile}

[github-actions]

Purely additive analytics instrumentation (new typed events, track() calls in loops UI) with no schema, API contract, billing, auth, or CI changes; the one substantive Greptile finding (builder-session count freezing early) is directly fixed in this diff via the new isSettled gating, and the author has STRONG familiarity with this code.

• Author wrote 90% of the modified lines and has 26 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	✓	353L, 7F substantive — within ceiling
tier	✓	T1-agent / T1d-complex (353L, 7F, single-area, feat)
stamphog 2.0.0b3		.stamphog/policy.yml @ f969fec · reviewed head ace377f

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

[github-actions]

Pure analytics instrumentation (new event definitions plus track() calls) with no data-model, API-contract, billing-logic, or security changes; the one Greptile concern about premature builder-session counting is fixed by the accompanying isSettled gating logic, and the change is well covered by new tests.

• Author wrote 90% of the modified lines and has 26 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	✓	366L, 8F substantive, 789L/10F incl. docs/generated/snapshots — within ceiling
tier	✓	T1-agent / T1d-complex (789L, 10F, single-area, feat)
stamphog 2.0.0b3		.stamphog/policy.yml @ f969fec · reviewed head 9ab43cf