CI lint checks install an unused rust toolchain (and it's flaky)

Nobody has claimed this yet.

### Describe the issue

The Rust bindings look dormant: https://github.com/microsoft/onnxruntime/issues/21533

1. The dedicated CI workflow for Rust was already removed in https://github.com/microsoft/onnxruntime/pull/19067, but this left lintrunner configs for the Rust bindings in the lint workflow.
2. The rustfmt check that was in the lintrunner config was removed in an unrelated PR: https://github.com/microsoft/onnxruntime/pull/24480
3. The Rust setup step (which was added for rustfmt in https://github.com/microsoft/onnxruntime/commit/e754edaecfca25ddd8dbf5a32ada1750dad6bf44) is still there: https://github.com/microsoft/onnxruntime/blob/01f0dba66cc5da8ad20ee81b1795b3b110ad913a/.github/workflows/lint.yml#L55 and https://github.com/microsoft/onnxruntime/blob/01f0dba66cc5da8ad20ee81b1795b3b110ad913a/.github/workflows/pr_checks.yml#L36.

The setup of this Rust toolchain (that I believe is unused) is apparently flaky, I guess because it needs to retrieve the software over the network on your CI runner. (Though it's also using an action from an archived unmaintained repo.)

* https://github.com/microsoft/onnxruntime/actions/runs/29509983242/job/87780658679?pr=29728
* https://github.com/microsoft/onnxruntime/actions/runs/29509983774/job/87780660680?pr=29728

### To reproduce

Run the CI & it'll fail sometimes, apparently

### Urgency

Not urgent

### Platform

Web Browser

### OS Version

Ubuntu

### ONNX Runtime Installation

Built from Source

### ONNX Runtime Version or Commit ID

adf13a736a3d3aabbba8fdb31db373a5117513c0

### ONNX Runtime API

Other / Unknown

### Architecture

X64

### Execution Provider

Other / Unknown

### Execution Provider Library Version

_No response_

Review .github/workflows/lint.yml and .github/workflows/pr_checks.yml, focusing on the Rust setup steps and remaining lintrunner configuration. Run the affected CI checks to confirm the unused Rust toolchain is no longer installed and that lint and PR checks complete successfully without the flaky setup.

Written by the indexing model from the issue text.