[vMCP] Consolidate duplicate identity-propagation round-trippers into shared internal transport package

Context

After the fix in #5323 (commits 2298d349 + 109a8a15), the identity-propagation round-tripper exists in two parallel implementations:

• pkg/vmcp/client/client.go — identityPropagatingRoundTripper (with isHealthCheck field; used by the per-call httpBackendClient).
• pkg/vmcp/session/internal/backend/mcp_session.go — identityRoundTripper (without isHealthCheck; used by the persistent-session connector).

The two types now have:

• Near-identical struct definitions (base, fallbackIdentity, with one carrying an extra isHealthCheck bool).
• Near-identical RoundTrip implementations, both gating fallback injection on !hasIdentity.
• Near-identical doc comments (each citing #5323).
• Near-identical unit test suites (both following the *_PerRequestIdentity_* / *_FallbackIdentity_* grouping).

The asymmetric health-check handling is documented in the identityRoundTripper doc comment, but the structural duplication remains a long-term maintenance hazard: any future change to the identity invariant (e.g. logging on fallback injection, metrics counters, additional checks) must be repeated in both files with no compile-time link between them.

Proposal

Extract both round-trippers into a small internal helper package — e.g. pkg/vmcp/internal/transport — and have both pkg/vmcp/client/client.go and pkg/vmcp/session/internal/backend/mcp_session.go consume the same type. Parameterise the health-check marker so the same implementation serves both call sites:

• Constructor option pattern (transport.WithHealthCheckMarker()) or
• Two thin wrapper types in the same package sharing a common implementation.

The consolidation should also unify the unit test suites in one package, removing the lock-step maintenance requirement.

Acceptance criteria

• Single round-tripper type (or family) lives in pkg/vmcp/internal/transport (or similar) and is consumed by both pkg/vmcp/client/client.go and pkg/vmcp/session/internal/backend/mcp_session.go.
• Health-check marker propagation is opt-in via a constructor option, not a separate type that the session-backend variant lacks.
• Unit test suite for the round-tripper(s) lives alongside the shared implementation; the consumer packages keep only integration-level tests that exercise the full transport chain.
• No behavioural change: existing pkg/vmcp/client/client_test.go, pkg/vmcp/session/internal/backend/roundtripper_test.go, and pkg/vmcp/session/internal/backend/mcp_session_identity_refresh_test.go continue to pass (or are migrated alongside the move).

Notes

This was raised as a MEDIUM finding on the iteration 2 review of #5323. The reviewer explicitly allowed deferring it from the bug-fix PR; this issue tracks the cleanup so the duplication is not silently forgotten.

Related: #5323

Start by comparing the round-tripper implementations in pkg/vmcp/client/client.go and pkg/vmcp/session/internal/backend/mcp_session.go, then review the related tests named in the acceptance criteria. Extract the shared implementation under pkg/vmcp/internal/transport with opt-in health-check marking, move its unit tests alongside it, and run the existing consumer tests to confirm no behavioral change.