fix(relay): preserve reconnect backoff

[cameronhotchkies]

Why

Manual relay recovery polls every three seconds, repeatedly consuming the session's exponential-backoff timer and leaving reconnect behavior stuck or noisy on degraded networks.

What

• Replace fixed-cadence Phase 3 polling with observation of the RelayClient background reconnect loop
• Raise the fast-path deadline above the native websocket timeout and enforce that contract in a regression test
• Keep the existing 120-second backstop as a soft UI timeout without stopping background retries

Risk Assessment

Medium — this changes live relay recovery timing, but removes a competing retry loop rather than adding one. The existing connection-state subscription remains the success signal.

References

• Stacked on refactor(relay): expose reconnect timing policy #2310 (lazyjoe/reconnect-testability-refactor)
• Investigation: RESEARCH/BUG_RELAY_RECONNECT_HANG.md
• just ci
• cd desktop && pnpm typecheck && pnpm check && pnpm test (3485 pass)
• git diff --check

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