feat(code): Set posthog-js project + organization groups

[Twixes]

Summary

We have a inbox-gated-due-to-scale flag to effectively put a more controlled waitlist. But it hasn't actually taken effect, because PH Code didn't set the group analytics properties.

Fixing by mirroring how the main PostHog frontend (userLogic.ts) attaches the user to project and organization groups via posthog.group(...) after identify. Groups update on login, project switch, and org switch. posthog.reset() on logout clears them.

---

Created with PostHog Code

[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
apps/code/src/renderer/features/auth/hooks/useAuthSession.ts:75-89
**Duplicated group-setting logic (OnceAndOnlyOnce)**

The 16-line block that calls `setUserGroup` for `"project"` and `"organization"` is copy-pasted verbatim into `authStore.ts` (lines 168–183). If the set of group properties ever needs to change (e.g. adding a `region` property to the project group), both places must be updated in sync. A small helper like `setUserGroups(user: { team?: ...; organization?: ... })` exported from `analytics.ts` (or a shared utility) would remove the duplication and make future changes a one-liner at both call sites.

_{Reviews (1): Last reviewed commit: "feat(code): set posthog-js project + org..." | Re-trigger Greptile}