[train] Use custom wheel for vllm-router for /chat/completions fix

[SumanthRH]

What does this PR do?

Addresses the issue with /chat/completions in the new inference codepath #1591 .

The issue is that vllm-router drops extra arguments (i.e arguments not in the OpenAI spec). I made a PR to fix this: vllm-project/router#162

While we wait for a new vllm-router release, we should ensure that SkyRL integrations that rely on /chat/completions don't break because of this.

This PR moves our vllm-router dependency to use a custom wheel built with cherry-picking the fix on top of the latest release (0.1.14). Wheel is currently built just for x86_64 arch for now.

[devin-ai-integration]

✅ Devin Review: No Issues Found

Devin Review analyzed this PR and found no potential bugs to report.

View in Devin Review to see 1 additional finding.

[gemini-code-assist]

Code Review

This pull request introduces a custom wheel for vllm-router to resolve an issue with the /chat/completions endpoint. The review feedback points out an inconsistency: the wheel is restricted to x86_64 architectures, which may cause users on other Linux platforms (such as ARM64) to unknowingly use the buggy version from PyPI. It is recommended to use a git source or provide wheels for other architectures to ensure the fix is applied consistently across all supported platforms.

[SumanthRH]

It looks like the official PyPI wheel has some additional steps to package the wheel, and unfortunately the steps are not listed in the README.

Seeing the following errors on CI (inspecting the vllm-router logs):

Process vllm-router:
Traceback (most recent call last):
  File "/home/ray/anaconda3/lib/python3.12/multiprocessing/process.py", line 314, in _bootstrap
    self.run()
  File "/home/ray/anaconda3/lib/python3.12/multiprocessing/process.py", line 108, in run
    self._target(*self._args, **self._kwargs)
  File "/home/ray/default/skyrl/backends/skyrl_train/inference_servers/vllm_router.py", line 44, in _run_router_with_logging
    launch_router(router_args)
  File "/home/ray/.cache/uv/builds-v0/.tmpkuayMU/lib/python3.12/site-packages/vllm_router/launch_router.py", line 52, in launch_router
    raise e
  File "/home/ray/.cache/uv/builds-v0/.tmpkuayMU/lib/python3.12/site-packages/vllm_router/launch_router.py", line 45, in launch_router
    raise RuntimeError("Rust Router is not installed")
RuntimeError: Rust Router is not installed

[SumanthRH]

GPU CI is passing: https://github.com/NovaSky-AI/SkyRL/actions/runs/25903325504/job/76131304194?pr=1601

I believe we are good to merge. For now. Will track building a wheel for ARM64 in an issue.