feat: trace FastMCP HTTP requests with OpenTelemetry

[lesnik512]

Why

FastMcpBootstrapper has logging, Sentry, Pyroscope, health checks and Prometheus, but no tracing: FastMcpConfig has no OpenTelemetryConfig and no instrument creates server spans. Ported from community-of-python/microbootstrap#152.

Design

FastMCP builds its ASGI application lazily, in http_app(). The user calls it after bootstrap, or run(transport="http") calls self.http_app(...) (in fastmcp 3.0 through 3.4). So nothing exists to instrument at bootstrap time. microbootstrap solves this by subclassing FastMCP, but lite-bootstrap receives the user's own instance. Instead:

• _postprocess_http_apps() overrides http_app on that instance only, passes every application it builds through a postprocessor, and returns an undo that teardown calls. Overrides chain, and teardown runs in reverse order, so the metrics PR stacked on this one can hook the same method.
• FastMcpOpenTelemetryInstrument adds OpenTelemetryMiddleware to each application. The span name and http.route come from the first Route/Mount that fully matches. Unmatched paths get a method-only span with no http.route.
• Exclusions use the same full-URL anchoring Litestar used before feat!: trace Litestar through its own OpenTelemetryPlugin #279: ^\w+://[^/]*/health(?:/|$), parsed with parse_excluded_urls, because asgi 0.49b0 cannot parse a string itself.
• Applications already carrying _is_instrumented_by_opentelemetry, the flag StarletteInstrumentor sets, are skipped, so a request is never traced twice.
• The anchoring helper is duplicated from the Litestar instrument on purpose. feat!: trace Litestar through its own OpenTelemetryPlugin #279 moves Litestar to path-based patterns, so there is no shared format left to hoist.

Changes

• FastMcpConfig includes OpenTelemetryConfig. No new required fields.
• New is_fastmcp_opentelemetry_installed probe, and a fastmcp-otl extra (otl plus opentelemetry-instrumentation-asgi>=0.49b0), included in fastmcp-all and in the install-isolation CI list.
• The floor smoke for fastmcp turns on OpenTelemetry and builds an http_app().
• Docs: FastMCP tracing section, installation table, metrics note.

Tests

• Exported spans for GET /health/ and POST /mcp carry http.route. An unmatched path gets a method-only span.
• The metrics path, the health path (with health spans off), configured URLs and both trailing-slash forms are excluded; the lookalike /custom-healthy is not.
• Every http_app() gets exactly one middleware, and instrumenting twice is a no-op. Teardown removes the override. The instrument is skipped without asgi instrumentation.
• just lint and just test pass (348 passed).
• Floor smoke passes (fastmcp==3.0.0, opentelemetry-instrumentation-asgi==0.49b0, Python 3.11). At those floors, real requests give GET /health/, POST /mcp and a bare GET for a 404, and /metrics is excluded.