fix(cli): route provider tests through connection API

[hydraxman]

Description

Aligns the provider-test CLI paths with the server's connection-owned management API.

• omniroute test now resolves a configured connection and calls POST /api/providers/{id}/test instead of the missing /api/v1/providers/test route.
• omniroute test --all-providers accepts the current { connections, total } response shape and carries exact connection ids into both non-interactive and TUI runs.
• omniroute providers test-all keeps existing local probes, but falls back to the server for custom API-key connections that the local probe table does not support.
• The TUI uses the shared API client so management authentication and timeout behavior stay consistent with the rest of the CLI.

Related Issue

Fixes #10570
Related to #10564. The separate rotation method mismatch remains owned by #10366.

Type of Change

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• Documentation update

Testing

• node --import tsx/esm --test tests/unit/cli-provider-test-routes-10570.test.ts tests/unit/cli-providers-command.test.ts tests/unit/cli-providers-rotate.test.ts tests/unit/cli-route-unavailable-fallback-10081.test.ts tests/unit/cli-expanded-commands.test.ts — 41 passed
• npm run test:vitest — 40 files, 362 tests passed
• npm run lint — passed
• npm run typecheck:core — passed
• npm run check:changelog-integrity — passed
• npm run check:docs-sync — passed
• npm run check:any-budget:t11 — passed
• npx prettier --check CHANGELOG.md bin/cli/commands/test-provider.mjs bin/cli/tui/ProvidersTestAll.jsx bin/cli/commands/providers.mjs tests/unit/cli-provider-test-routes-10570.test.ts — passed
• npm run test:unit — did not complete within a 600-second local ceiling; the current release branch has an active base-red report for full-suite hangs/failures in 🔴 Release branch not green: release/v3.8.50 #9985. The focused Node suite and Vitest suite above completed successfully.

After publication, four CI jobs failed: Docs Gates (fast-path), Fast Quality Gates, and unit shards 1/4 and 3/4. Fast Quality Gates reports the current-base public-creds and mutation-test-coverage gates tracked in #9985. I reproduced both failing unit shards locally with the exact CI command: shard 1 passed 7,619 tests and failed three untouched dependency/config/catalog tests; shard 3 passed 7,493 tests and failed eight untouched Alibaba quota-classification, call-log rotation, docs-count, CLI-catalog-count, and ServiceSupervisor tests. The strict docs-count failure is the same current-base drift tracked in #9985; none of the failing tests or source owners are changed by this PR.

Checklist

• My code follows the project's style guidelines
• I have performed a self-review of my own code
• I have added tests that prove my fix is effective
• New and existing unit tests pass locally with my changes in the focused scope
• I have updated the changelog
• I have read and followed the contribution guidelines

Contributions

Made by Nathan.

[diegosouzapw]

Looks solid — verified /api/v1/providers/test doesn't exist and /api/providers/{id}/test does, ran the full stated focused test matrix (41/41 pass) locally. Will re-check the 4 CI jobs you flagged as base-red against current #9985 state before merge, otherwise this is ready to go. Thanks for the thorough test coverage.