test(router-proxy): pin the metrics endpoint to the llmkube registry

[Defilan]

What

A regression test pinning the router-proxy metrics endpoint to the registry the
llmkube collectors actually register into, plus the small extraction that makes
it testable.

Why

Refs #1427

The fix this PR originally carried is already on main. #1393 landed it while
this was open, so all that remains, and the part that was missing, is a test.

The endpoint added in #1457 wired promhttp.Handler(), which serves
prometheus.DefaultGatherer, while internal/metrics registers every collector
into ctrlmetrics.Registry. Different registries, so it exposed none of
llmkube_router_* or llmkube_modelpool_*.

That is worth a test rather than care, because the failure is silent in every
direction: the scrape returns HTTP 200, the PodMonitor from #1473 reports a
healthy target, and the dashboards are just empty. It survived review and a
merge for exactly that reason. Measured on the built binaries at the time: 38
metric families under the default registry, 149 under controller-runtime's.

How

One detail is load-bearing. The test increments a real router counter before
scraping, because a labelled collector emits no family until it has a child
series, so an idle scrape is byte-identical under either registry and the
obvious version of this test passes on the bug.

I verified that by reintroducing promhttp.Handler() and confirming the test
fails, then restoring the fix and confirming it passes. A regression test nobody
has watched fail is not yet a regression test.

newMetricsHandler() is extracted from main() only so there is something to
assert against; the behaviour is unchanged from what #1393 landed.

Credit

The underlying bug was found by @sylvainsf while rebasing #1393. This PR was
opened to carry the fix separately, and has been repurposed to the test now that
their fix has merged.

Testing

go test ./cmd/router-proxy/, make lint 0 issues, and the fails-without-the-fix
check described above.

Checklist

• Tests added/updated
• make test passes locally
• make lint passes locally
• Commit messages follow conventional commits
• All commits are signed off (git commit -s) per DCO
• AI assistance (if any) is disclosed above
• Documentation updated (if user-facing change) — none needed, no behaviour change

Assisted-by: Claude Code (wrote the test and the extraction, and ran the
two-binary comparison and the fails-without-the-fix validation)

[codecov]

Codecov Report

❌ Patch coverage is 66.66667% with 1 line in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
cmd/router-proxy/main.go	66.66%	1 Missing ⚠️

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