Fork: Chrome/macOS login fix + exit-node picker & management UI

Hi! 👋

I reworked this extension to get it running smoothly on Chrome / macOS and added a few things that have come up in issues here. Sharing in case it's useful to others.

What I changed / added

• Working login on Chrome/macOS — the popup's "Log in" link was a dead anchor (#login with no handler); it now opens the auth flow. Also fixed Chrome-vs-Firefox detection during --install (newer Chrome also defines browser, so the install command was wrongly generated as Firefox).
• Exit-node picker — pick or clear a per-profile exit node right from the popup (related: #5, #3).
• Management page at http://100.100.100.100/ — device status, tailnet machine list (address / OS / online), exit-node selector, and a Log out button, so logging out no longer requires removing & re-adding the extension.
• Honest transient states — "Connecting…" / "Waiting for approval…" while the link comes up, instead of an error flash right after login.
• Shipped the missing need-install icon and added a live popup refresh after login.

Repo: https://github.com/iazat/ts-browser-ext

If you'd like, I'm happy to split any of these into focused PRs against this repo — just say which ones are interesting and I'll send them in.

This is a multi-part fork proposal rather than a focused change. Start by reviewing the popup login flow and --install browser detection, then assess the exit-node and management UI work against issues #5 and #3. Done would require a maintainer-selected scope and separate acceptance criteria for the chosen part.