Draft follow-up tidy-ups: configurable stdio probe timeout + IsStatefulSession/IsMrtrSupported gate review

[halter73]

Follow-up from #1610. Two small carried-over cleanups:

1. Configurable stdio probe timeout

The stdio sessionless-probe timeout is hard-coded to 5 s. Make it configurable (transport option) so callers can tune it for slow-starting servers / CI.

2. IsStatefulSession() / IsMrtrSupported gate review

McpServerImpl.IsMrtrSupported carries a TODO to revisit how it gates on IsStatefulSession(). Review whether the MRTR-support determination is correct now that stateful mode is effectively stdio-only under the draft changes.

cc #1610

[halter73]

Deep-dive: precise pointers + recommendation

Recommendation: keep both as follow-ups (neither is a clean mechanical fix for #1610).

1. Configurable stdio probe timeout

• Hard-coded at McpClientImpl.cs:313 — var probeTimeout = TimeSpan.FromSeconds(5); (capped by InitializationTimeout at lines 309-318).
• Making it configurable means adding public API surface (e.g. a SessionlessProbeTimeout on McpClientOptions or StdioClientTransportOptions). That deserves its own focused PR with API-surface review + naming + ApiCompat/docs, and is unrelated to the session-id removal that Default draft protocol support: sessionless + handshake-less (SEP-2575 + SEP-2567) #1610 is scoped to. Don't bundle.

2. IsMrtrSupported / IsStatefulSession() gate review

• Current logic: McpServerImpl.cs:1660 — public override bool IsMrtrSupported => ClientSupportsMrtr() || IsStatefulSession(); with IsStatefulSession() at cs:1656 (_sessionTransport is not StreamableHttpServerTransport { Stateless: true }).
• The TODO that motivates this item is at McpServerImpl.cs:1702 (TODO(stateless-draft): When 2026-07-28 becomes stateless-only, the IsStatefulSession() gate collapses).
• This is a review/cleanup tied to a future spec milestone (draft going stateless-only), not an actionable change today — the current gate is intentionally still honoring legacy stateful MRTR. Revisit when the draft revision drops the stateful back-compat path; the IsStatefulSession() disjunct then becomes dead and can be removed.

Neither belongs in #1610. Leaving both here as tracked follow-ups.

[halter73]

These were both addressed as part of #1610 in the end.