Add posthog frontend

[nezaj]

Following up from #2138, this passes along the info from our SDKs and dashboard so we can track events in Posthog.

Here's an overview of the events we'll track

Event	Description	Sources
auth:complete	User completed OAuth login	instant-cli, create-instant-app
app:create	Permanent app created	instant-cli, dashboard, platform-sdk
app:create-ephemeral	Temporary app created (anonymous)	create-instant-app
app:claim	Ephemeral app converted to permanent	create-instant-app
app:delete	App marked for deletion	dashboard, platform-sdk
app:clear	App data cleared	dashboard
schema:push	Schema deployed	instant-cli, dashboard, platform-sdk
schema:pull	Schema fetched	instant-cli
perms:push	Permissions deployed	instant-cli, dashboard, platform-sdk
perms:pull	Permissions fetched	instant-cli

For create-instant-app we'll also track the following which can be useful for understanding what tools are users are vibing with

Property	Description
template	Base template used: next-js-app-dir, vite-vanilla, or expo
aiTool	AI tool rules added: cursor, claude, codex, gemini, zed, windsurf, or none
usedAiPrompt	Whether --ai flag was used to generate code with Claude Code

Tested events using instant-cli, create-instant-app and the dashboard and saw them all flowing into Posthog. Pretty neat!

[github-actions]

View Vercel preview at instant-www-js-add-posthog-frontend-jsv.vercel.app.

[stopachka]

Niice!

[stopachka]

Niice!