Pull request automation: use full npm install

[sirreal]

What?

Use full npm install for the pull-request-automation workflow.

This installation is larger and slower, however I suspect that is likely to be offset by caching.
This is also blocking work on the migration to npm workspaces that has its own merits in #66272.

Why?

The pull-request-automation workflow creates problems when migrating to npm workspaces:

https://github.com/WordPress/gutenberg/actions/runs/11435991643/job/31813748278

Extracted from #66272.

How?

Use the regular npm installation flows shared by other github actions in the project.

Testing Instructions

CI passes. pull-request-automation workflow runs as expected.

[sirreal]

The job on this branch reuses a cache and completes in a reasonable amount of time. It just took 37s. It doesn't appear significantly slower than other recent runs. They range from 17s to 32s.

[github-actions]

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Co-authored-by: gziolo <[email protected]>

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[gziolo]

I don't think to make sense anymore to have a different installation step for this job given that the cache reuse is so fast.

[getdave]

Backporting this on advice from @sirreal in relation to failing CI on the wp/6.7 branch

cc @kevin940726 @ellatrix @cbravobernal

[github-actions]

There was a conflict while trying to cherry-pick the commit to the wp/6.7 branch. Please resolve the conflict manually and create a PR to the wp/6.7 branch.

PRs to wp/6.7 are similar to PRs to trunk, but you should base your PR on the wp/6.7 branch instead of trunk.

# Checkout the wp/6.7 branch instead of trunk.
git checkout wp/6.7
# Create a new branch for your PR.
git checkout -b my-branch
# Cherry-pick the commit.
git cherry-pick e43a1c574959eb835f34b92479b7b6b4ff5ff8ea
# Check which files have conflicts.
git status
# Resolve the conflict...
# Add the resolved files to the staging area.
git status
git add .
git cherry-pick --continue
# Push the branch to the repository
git push origin my-branch
# Create a PR and set the base to the wp/6.7 branch.
# See https://docs.github.com/en/pull-requests/collaborating-with-pull-requests/proposing-changes-to-your-work-with-pull-requests/changing-the-base-branch-of-a-pull-request.

[getdave]

Ok then...I'll do this by hand.

[getdave]

Manually backported in #66447