Use prek in documentation and CI (#22505)

## Summary

AFAIK, many of us on the team are using prek now. It seems appropriate
to modify the docs to formalize it.

.github/workflows/ci.yaml

@@ -769,8 +769,8 @@ jobs:
       - name: "Remove wheels from cache"
         run: rm -rf target/wheels
 
-  pre-commit:
-    name: "pre-commit"
+  prek:
+    name: "prek"
     runs-on: ${{ github.repository == 'astral-sh/ruff' && 'depot-ubuntu-22.04-16' || 'ubuntu-latest' }}
     timeout-minutes: 10
     steps:
@@ -784,17 +784,17 @@ jobs:
       - uses: actions/setup-node@395ad3262231945c25e8478fd5baf05154b1d79f # v6.1.0
         with:
           node-version: 24
-      - name: "Cache pre-commit"
+      - name: "Cache prek"
         uses: actions/cache@9255dc7a253b0ccc959486e2bca901246202afeb # v5.0.1
         with:
-          path: ~/.cache/pre-commit
-          key: pre-commit-${{ hashFiles('.pre-commit-config.yaml') }}
-      - name: "Run pre-commit"
+          path: ~/.cache/prek
+          key: prek-${{ hashFiles('.pre-commit-config.yaml') }}
+      - name: "Run prek"
         run: |
           echo '```console' > "$GITHUB_STEP_SUMMARY"
-          # Enable color output for pre-commit and remove it for the summary
-          # Use --hook-stage=manual to enable slower pre-commit hooks that are skipped by default
-          SKIP=cargo-fmt uvx --python="${PYTHON_VERSION}" pre-commit run --all-files --show-diff-on-failure --color=always --hook-stage=manual | \
+          # Enable color output for prek and remove it for the summary
+          # Use --hook-stage=manual to enable slower hooks that are skipped by default
+          SKIP=cargo-fmt uvx prek run --all-files --show-diff-on-failure --color always --hook-stage manual | \
             tee >(sed -E 's/\x1B\[([0-9]{1,2}(;[0-9]{1,2})*)?[mGK]//g' >> "$GITHUB_STEP_SUMMARY") >&1
           exit_code="${PIPESTATUS[0]}"
           echo '```' >> "$GITHUB_STEP_SUMMARY"