[Rust Frontend] Add /pause, /resume, /is_paused endpoints

[sahilsGit]

Purpose

Adds POST /pause, POST /resume, and GET /is_paused to the Rust frontend,
contributing to "RL / admin / lifecycle APIs" in the Rust frontend roadmap
(#44280).

Route	Utility call	Args	Response
POST /pause	pause_scheduler	(mode, clear_cache)	{"status": "paused"}
POST /resume	resume_scheduler	()	{"status": "resumed"}
GET /is_paused	is_scheduler_paused	()	{"is_paused": <bool>}

Changes:

• engine-core-client: add pause_scheduler, resume_scheduler, and
  is_scheduler_paused client methods (the latter mirrors is_sleeping's
  cross-engine consistency check).

• server: new routes/pause.rs with the three handlers; registered in the
  dev-mode block alongside the other Rust admin routes.

• The deprecated Python wait_for_inflight_requests flag is intentionally
  omitted in favor of mode="wait" (noted with a TODO).

Test Plan

cargo fmt --all --check
cargo clippy -p vllm-server -p vllm-engine-core-client --all-targets -- -D warnings
cargo nextest run -p vllm-server                    # full server suite (no regressions)
cargo nextest run -p vllm-engine-core-client        # full client suite
cargo nextest run -p vllm-server pause_route resume_route is_paused_route admin_routes_are_hidden

New tests in rust/src/server/src/routes/tests.rs (each asserts the engine
receives the correct utility method name + args):

• pause_route_uses_python_compatible_default_query_values — POST /pause with
  no params sends pause_scheduler with ["abort", true], returns
  {"status": "paused"}
• pause_route_rejects_invalid_mode — POST /pause?mode=banana → 400
  (invalid_request_error, param mode), engine never contacted
• resume_route_sends_no_args — POST /resume sends resume_scheduler with no
  args, returns {"status": "resumed"}
• is_paused_route_returns_json_payload — GET /is_paused sends
  is_scheduler_paused, returns {"is_paused": true}
• extended admin_routes_are_hidden_when_dev_mode_is_disabled to assert
  /pause, /resume, /is_paused return 404 when dev-mode is off

Test Result

cargo nextest run -p vllm-server pause_route resume_route is_paused_route admin_routes_are_hidden
  → Starting 5 tests across 1 binary (154 tests skipped)
    PASS pause_route_uses_python_compatible_default_query_values
    PASS pause_route_rejects_invalid_mode
    PASS resume_route_sends_no_args
    PASS is_paused_route_returns_json_payload
    PASS admin_routes_are_hidden_when_dev_mode_is_disabled
  → Summary: 5 tests run, 5 passed, 154 skipped

---

Essential Elements of an Effective PR Description Checklist

• The purpose of the PR, such as "Fix some issue (link existing issues this PR will resolve)".
• The test plan, such as providing test command.
• The test results, such as pasting the results comparison before and after, or e2e results
• (Optional) The necessary documentation update, such as updating supported_models.md and examples for a new model. Not needed — Rust-frontend API wiring with no model/docs surface.

[github-actions]

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🚀

[BugenZhao]

@codex review

[chatgpt-codex-connector]

Codex Review: Didn't find any major issues. Keep them coming!

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[BugenZhao]

LGTM