feat(analytics): E-02 track installs and updates and open the welcome page

[navidshad]

What

• chrome.runtime.onInstalled now sends one Mixpanel event on the install's analytics id:
  • extension_installed (reason install)
  • extension_updated with previous_version (reason update)
  • A Chrome update is ignored.
• If the install id does not exist yet, it is created with the same key (analyticsAnonymousId) and format as src/plugins/mixpanel.ts.
• On a first install it opens:
  https://subturtle.app/?install_id=<install id>&utm_source=extension&utm_medium=install

Why

There was no install event anywhere. The landing page could not be joined to the install that follows it. Work list: subturtle-doc docs/tech/analytics-fixes-implementation.md (row E-02).

Service worker safety

• mixpanel-browser needs window and document. A MV3 service worker has neither. So the background sends the event with fetch to Mixpanel's /track endpoint (through MIXPANEL_API_HOST), in the same shape mixpanel-browser uses.
• The listener is added at the top level, so Chrome finds it when it wakes the worker.
• A failed request or a failed tab open is logged and never throws.

One change from the work list

The welcome page opens only for Web Store installs (the manifest has update_url). Unpacked builds (local dev, the CI e2e run, a dev zip) still send the event but do not open subturtle.app. This stops dev reloads and CI runs from opening the site and counting fake installs on the landing page.

How tested

• New unit tests: tests/install-tracking.test.ts (install, update, existing id, Chrome update ignored, unpacked build, failed request, URL encoding).
• yarn typecheck: clean.
• yarn test: 41 files, 365 tests pass.
• yarn build: OK.
• The repo has no lint script.

Dependencies

• Pairs with landing row D-01 (feat(landing): D-01 track extension_installed from the post-install link subturtle-dashboard-app#144), which reads install_id from the URL.
• This PR and fix(analytics): E-01 E-05 send the install id and trigger with translation calls #58 both add src/common/helper/install-id.ts with the same content, so they merge in either order. fix(analytics): E-01 E-05 send the install id and trigger with translation calls #58 also makes mixpanel.ts use this helper; this PR leaves mixpanel.ts alone so it stays independent.

🤖 Generated with Claude Code

[navidshad]

Replaced by #62, which combines all extension rows (E-01 to E-06) into one PR.