Serve MCP 2026-07-28 stateless requests through the transparent proxy

[jhrozek]

Part of #5755. Design: RFC THV-0081; arch doc §Changes → "Transparent proxy" (branch stateless-transport-proxies-design, PR #5808).

Serve Modern (2026-07-28) stateless requests through the transparent (HTTP→HTTP) proxy.

Changes

• Wire ClassifyRevision (store the resulting Revision in session metadata so RoundTrip reads one field).
• Gate the initialize-triggered machinery on Legacy — session guard, pod-pinning, init-body storage, re-init replay, and backend-SID rewrite — so a Modern request collapses to a plain reverse proxy (Go's http.Transport correlates responses natively; no shared pipe).
• Modern health readiness: the internal monitor must not use the ping-based StatelessMCPPinger (ping is removed in 2026-07-28 and a Modern-only backend rejects it) — gate off server/discover / first successful backend contact, and never default the gate ready.
• Make the GET/DELETE gate revision-aware so it does not 405 a Legacy client's SSE stream on a dual-era endpoint (reconcile with the existing --stateless flag).

Dependencies

Depends on #5755 foundation issue (the deepened classifier).

Verification

• Modern request to a multi-replica backend routes without pod-pinning and does not re-initialize on a backend 404.
• A Modern request carrying a foreign session header is not rewritten onto a pinned backend.
• Pinger-vs-Modern-backend test (the removed-ping case).
• Legacy sticky behavior unchanged; the internal monitor does not self-terminate on a cold-starting Modern backend.

May split gating and health into separate PRs.