[Frontend] Accept the model path that /v1/models publishes

[TyroneNel]

Purpose

/v1/models publishes the checkpoint path of each entry in root:

{"id":"my-model","root":"/models/my-checkpoint","max_model_len":150000}

OpenAIServingModels.is_base_model matches the served name only (any(model.name == model_name ...)). A client that sends root back gets a 404. The value came from the API itself, so the 404 is not expected.

is_base_model now accepts the served name, the full model path, or the basename of that path. All three are exact matches. There is no prefix match and no fuzzy match. An unknown name still returns 404.

Test Plan

• Manual, against a v0.28.0 server whose id and root are different: request the model by name, by root, and by basename. The "after" server runs v0.28.0 with this change applied as a patch (the same code change).
• pre-commit run on the changed file.

Test Result

Before (id = my-model, root = /models/my-checkpoint):

model="my-model"               -> 200
model="/models/my-checkpoint"  -> 404 The model `...` does not exist.
model="my-checkpoint"          -> 404 The model `...` does not exist.

After (live server, id = qwen3.8-27b; I shortened the local path to <dir>/<checkpoint>):

model="qwen3.8-27b"                  -> 200
model="/app/models/<dir>/<checkpoint>" -> 200
model="<checkpoint>"                 -> 200
model="not-a-served-model"           -> 404 The model `not-a-served-model` does not exist.

pre-commit: 13 hooks passed, 0 failed

If you prefer to keep the name space strict, #58024 and #58025 already make the failure clear, and you can close this PR.

[claude]

Claude Code Review

This pull request is from a fork — automated review is disabled. A repository maintainer can comment @claude review to run a one-time review.

[github-actions]

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[TyroneNel]

I pushed a small update:

• Rebased on current main. No conflicts, and the change is the same.
• DCO. The commit now has a sign-off that matches the author, so the DCO check passes.
• pre-commit passes on the changed file (13 hooks).
• Live output. The PR body now shows the "after" rows from a running server.

When you have time, could a maintainer add the ready label, so that CI can run? Thank you!

[TyroneNel]

Hi! I rebased this PR on current main (b721a4c70).

What changed:

• The branch is now on top of main. The rebase had no conflicts.
• The diff is the same as before. The patch ID did not change.
• The commit keeps its DCO sign-off.

What I checked:

1. ruff check (v0.14.0, the pre-commit pin) passes on vllm/entrypoints/openai/models/serving.py.
2. ruff format --check passes on the same file.
3. The file compiles.

Status of CI: The pre-run-check job fails. The cause is not the code. The job needs the ready or verified label on the PR.

Request: When you have time, please add the ready label. Then CI can run the full suite.

Thank you for your time!