A signed-out 404 offers sign-in that comes back to the same address #4111

Seen on production: a signed-out visitor to a private repository's link gets '404 Nothing here … or is not visible to you' and only 'Go home'. The way back for the owner, who is just signed out, is missing.

Done:

• [ ] notFoundPage (src/web/chrome.ts) adds 'Sign in' as a btn to /signin?next= with the requested path and query when there is no session, for GET requests only.
• [ ] A signed-in 404 is unchanged, and the page still does not reveal whether the thing exists.
• [ ] Tests: signed-out GET of a private repository carries the link with the right next; signed in, no link; safeNext refuses another origin.

Files: src/web/chrome.ts, a test. Before pushing: bun x tsc --noEmit and the tests you touched.

Parked by the crew: the check failed ("origins on the web > /go/:code redirects a signed-out phone, and dead codes are one 404") and the decider saw no point in another try (pull #4114 closed). Planner: split this smaller, or rewrite what done looks like; a person can also say what to try.

Replaced by #4139.