Suggestion

Splitting out of #11204: right now, each CI job typically spends over a minute in the Install step:

Examples from a docs-only PR, #11200:

• https://github.com/typescript-eslint/typescript-eslint/actions/runs/14972488668/job/42056678571?pr=11200 took 57s
• https://github.com/typescript-eslint/typescript-eslint/actions/runs/14972488668/job/42056678626?pr=11200 took 1m 15s

That seems very long to me. In theory this should all be cached nicely, so all CI needs to do is download a lockfile and run a bit of disk linking/processing. Why does this take a full minute? Can we speed it up?

Additional Info

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