feat(mcp): record metrics for backend notification streams

[sangkyoonnam]

Description

Legacy backend notification GETs had no lifecycle metrics. Client heartbeats keep going after backend streams end, while failures are either silent (202/204/405, unexpected EOF) or only logged with the backend name.

This adds four backend-scoped instruments, all with mcp.backend, recorded in sendRequestPerBackend for GET only:

• mcp.notification_stream.open.attempts: counted before client.Do.
• mcp.notification_stream.open.outcomes with mcp.notification_stream.outcome: opened, unsupported (202/204/405, or a single JSON-RPC message in reply to the GET), http_4xx, http_5xx, http_other, transport_error, cancelled (before the stream opened). One outcome per completed opening attempt; a non-200 status keeps its class even when decoding the body fails.
• mcp.notification_stream.active: up/down counter, +1 on open and -1 on end.
• mcp.notification_stream.duration (seconds) with mcp.notification_stream.end_reason: eof, cancelled, error. A malformed final event, which the parser returns joined with io.EOF, counts as error.

The end reason is a dimension on the duration histogram rather than a separate counter; its count gives closes per reason. http_other keeps 201 and 3xx out of the 4xx/5xx buckets. Modern subscriptions/listen isn't proxied yet, so it is out of scope. If the existing eventChan send blocks after the client leaves, active stays above zero for that stream. POST requests, existing metrics, logs and return values are unchanged.

Tests use a real ManualReader: one healthy and one 405 backend in the same session, all backend streams ending while client heartbeats continue (active back to 0), status classes, single JSON-RPC responses, body-read and gzip failures, transport errors, unexpected and malformed final events, cancellation before and after open, and no notification-stream metrics for POST. make precommit and make test pass.

Per the generative AI policy: this change was developed with AI assistance (Claude Code). I have reviewed it, understand it, and take full ownership of the code, tests, and this description.

Related Issues/PRs (if applicable)

Fixes #2725
Related PR: #2733 (backend initialization metrics; no shared changed files)

Special notes for reviewers (if applicable)

The metric and attribute names, the http_other value and the histogram bounds (0.1s to 2h) are open to change if you'd rather match another convention.

[netlify]

✅ Deploy Preview for theagentrouter canceled.

Name	Link
🔨 Latest commit	f72bb8a
🔍 Latest deploy log	https://app.netlify.com/projects/theagentrouter/deploys/6abf663c5eeaaf00087c141b