RSPEED-3444: fix REST API metrics middleware route discovery and root_path handling

[anik120]

Description

Type of change

• Refactor
• New feature
• Bug fix
• CVE fix
• Optimization
• Documentation Update
• Configuration Update
• Bump-up service version
• Bump-up dependent library [pyproject.toml + uv.lock]
• Bump-up dependent library [requirements.*.txt for Konflux]
• Bump-up library or tool used for development (does not change the final image)
• CI configuration change
• Konflux configuration change
• Unit tests improvement
• Integration tests improvement
• End to end tests improvement
• Benchmarks improvement

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• If it is a core feature, I have added thorough tests.

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[anik120]

cc: @tisnik

[anik120]

Wow CI is very red but looking at all the recent 0.6 merges (eg #2656) I'm guessing we're just letting it be

I can't tell why e2e borks after 5s immediately either, it just has

Run echo "=== Configuration Summary ==="
=== Configuration Summary ===
Deployment mode: library
Environment: ci
E2E shard (Makefile test-e2e-tagged): not @skip and (@cfg_rh_identity or @cfg_negative or @cfg_byok_pdf or @cfg_degraded or @cfg_unified)
Source config: tests/e2e/configs/run-ci.yaml

=== Configuration Preview ===
Providers: 19
Models: 3

=== lightspeed-stack.yaml ===

and no other info

[tisnik]

LGTM