The 404 page offers a search for what was asked, and a stranger Create an account beside Sign in #8483

Intent: a wrong link is one tap from what the reader meant.

Today: /nope answers "Nothing here" with Sign in, Go home and Explore (src/web/chrome.ts notFoundPage); there is no way to look for the thing and no way to join.

Done:

• A GET 404 that is not plain carries a "Search for ‘<last path segment>’" button to /search?q=<segment>, the segment URL-decoded, trimmed to 100 characters, escaped; none when the segment is empty or the path is /.
• Signed out, Create an account (to /signup) sits beside Sign in; signed in, neither shows.
• plain 404s (a dead /go/:code) stay as they are: reveal nothing.
• Tests assert both buttons, the escaping of a segment like <x>, and the plain case.

Files: src/web/chrome.ts, a test. Risk: run bun scripts/design-lint.ts.