Use danielparks/github-actions/prek-auto-update.

[danielparks]

No description provided.

[claude]

Clean refactor. The logic is equivalent to what was inline — extracting it into a reusable composite action makes sense especially if the same pattern is used across repos.

A few observations:

• The action is pinned by commit SHA, which is the right practice.
• The actions/checkout bump (v6.0.2 → v6.0.3) is a nice bonus.
• The taiki-e/install-action inside the composite action is v2.81.6, up from v2.79.10 in the old inline step.
• The commit message inside the action gains a trailing period (```prek auto-update.) vs the original without one — minor but worth knowing if you care about consistency.
• The added inline permission comments (# Change files, # Create and update PRs) are a nice clarity improvement.

No blocking concerns.