`hermes mcp login`, the dashboard re-auth (web_server_mcp.py) and the Desktop
re-auth (tui_gateway/mcp_oauth_sessions.py) each bounded the login probe at
`max(connect_timeout, 315)`. The 315 was the default 300 s callback window
plus headroom, frozen: a user who set `oauth: {timeout: 3600}` still had the
probe cancelled at 315 s. That expiry was a bare `asyncio.TimeoutError`, whose
`str()` is '', so the CLI printed a blank `✗ Authentication failed:` line
(#116278, reporter's steps 5).
`tools/mcp_oauth.py::login_connect_timeout(config)` computes the bound once —
`max(connect_timeout, oauth.timeout + 15)` — and all three call sites use it.
`_probe_single_server` re-raises its wait_for expiry as a TimeoutError naming
the server, the elapsed bound and both governing knobs, so every caller's
`humanized or exc` renders a reason.
Slimmer redo of the blank-line half of #114527 (@liuhao1024): that PR races
the connect against `asyncio.wait` so an inner exception can win; with the
window now sized from oauth.timeout the callback waiter's own
`OAuth callback timed out` message wins on its own, and the described
TimeoutError covers the remaining case in one place.
Completes the timeout atom of #116278 (closed by #116658); refs #103633
Co-authored-by: liuhao1024 <sunsky.lau@gmail.com>
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