chore(app): Rename PostHog Code to PostHog

[charlesvien]

Problem

The product is now called just "PostHog", but the app still says "PostHog Code" everywhere (menu bar, About, window title, packaged bundle, UI copy).

Changes

Renames every user-visible surface: productName/executableName (bundle builds as PostHog.app), app.setName, menu bar, About, window titles, notifications, ~40 UI copy strings, mobile app name. Copy where bare "PostHog" would be ambiguous or false (HIPAA line, spend tiles, billing modal, OAuth callback pages) is rephrased instead of find-replaced.

Nothing load-bearing changes: appId (com.posthog.array), userData path, deep-link scheme, analytics/billing identifiers, feature flags and release artifact filenames are untouched, so auto-update, Keychain and dashboards keep working. On macOS the transition update renames the installed bundle on disk (PostHog Code.app becomes PostHog.app), verified in the update e2e; Squirrel cannot auto-relaunch across the rename, so after this one update the app stays closed until the user reopens it. Windows updates land in the existing install directory and keep the old folder name.

The forge update e2e now genuinely exercises the rename-upgrade path (old "PostHog Code" build updating into the renamed build); fixtures were updated to launch the renamed post-swap binary and match both process names.

Deferred to follow-ups: git-visible branding (Generated-By trailer, PR footer), backend usage-limit error string coordination, artifact filename rename, Discord portal app name.

How did you test this?

• pnpm typecheck, Biome, host-boundary check all green
• Unit suites: apps/code (337), workspace-server (748), core (2424), agent (1403), shared, git, ui
• pnpm --filter code package produces out/mac-arm64/PostHog.app with correct CFBundleName/CFBundleExecutable and unchanged CFBundleIdentifier + posthog-code URL scheme (verified via plutil)
• Packaged-app Playwright e2e: 13/13 pass (app name, window title, single-instance lock, userData path unchanged)
• Launched the dev app: window and menu bar show "PostHog (Development)"
• Update e2e (code-update-e2e.yml) needs a CI run with Apple signing; will trigger on this branch

Automatic notifications

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

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[github-actions]

React Doctor found no issues in the changed files. 🎉

_{Reviewed by React Doctor for commit b081d0b.}

[greptile-apps]

Too many files changed for review. (130 files found, 100 file limit)

Bypass the limit by tagging @greptile-apps to review.

[stamphog]

Gates denied this PR: it touches CI/CD workflows, auth-related files, billing code, and toolchain dependencies across 130 files — all matching deny-list categories. This needs human review before auto-approval.

[charlesvien]

@greptile-apps