Honor persisted PWA install status (#260)

[baixiangcpp]

Summary

• share the installed-state reader used by the global install CTA and Install App page
• recognize persisted appinstalled evidence after a normal browser-tab reload
• let a fresh beforeinstallprompt clear stale evidence and restore the native Install now CTA
• cover the persisted-to-fresh-prompt transition with a component regression test

Validation

• 7 focused test files, 40 tests
• npm run check:types
• targeted ESLint
• real Chromium reload and fresh-prompt regression on localhost
• npm run build
• npm run test:e2e:pwa
• git diff --check
• independent code review: no findings

Refs #260

The issue remains open for physical Android Chrome and iPhone Safari install-to-home-screen, standalone, airplane-mode offline, cache-clear, and real deployed-update evidence.

[baixiangcpp]

@codex review

[chatgpt-codex-connector]

Codex Review: Didn't find any major issues. What shall we delve into next?

Reviewed commit: a2e23101c0

ℹ️ About Codex in GitHub

Your team has set up Codex to review pull requests in this repo. Reviews are triggered when you

• Open a pull request for review
• Mark a draft as ready
• Comment "@codex review".

If Codex has suggestions, it will comment; otherwise it will react with 👍.

Codex can also answer questions or update the PR. Try commenting "@codex address that feedback".

[cloudflare-workers-and-pages]

Deploying byteflow with    Cloudflare Pages

Latest commit:	a2e2310
Status:	✅  Deploy successful!
Preview URL:	https://4deeda80.byteflow-c58.pages.dev
Branch Preview URL:	https://fix-issue-260-persisted-inst.byteflow-c58.pages.dev

View logs