Improve connection diagnostics and user-facing error states

[JSvandijk]

Summary

When connection or pairing fails, the project needs clearer diagnostics for users and maintainers.

Goal

Add more explicit states and error messages for cases like:

• unreachable host
• invalid base URL
• TLS/certificate problems
• pairing failures
• proxy target unavailable

Why this matters

Better diagnostics improve first-run success and make bug reports much easier to act on.

Possible scope

• clearer Android UI copy
• improved proxy error output
• troubleshooting documentation updates

[JSvandijk]

Closed on main in 52a7e5f. User-facing connection diagnostics were tightened across the Android wrapper, proxy, and docs, and the update/release path now has stronger validation so more failure cases are caught before shipping.

[hogeheer499-commits]

Rechecked this diagnostics track while preparing the upstream T3 discussion in pingdotgg/t3code#2514. Current validation from a fresh local checkout after npm install:

• npm test passed
• JS syntax checks passed
• ESLint passed
• manifest.json check passed
• release checks passed for version 1.1.0
• HTML tests passed: 18/18
• proxy smoke test passed

The implemented diagnostics remain relevant to the upstream proposal: Android has copyable HTTP/SSL/network diagnostics, and the optional proxy exposes GET /__t3mobile/health with upstream reachability and latency. Follow-up maintenance is tracked separately in #17 for proxy deployment guidance and #19 for keeping the lint/tooling path current.