CI will break whenever subosito/flutter-action is updated

_↴ Ported from [flutter/genui#818](https://github.com/flutter/genui/issues/818) — originally opened by [andrewkolos](https://github.com/andrewkolos) on 2026-03-20._
_Original labels: P2, front-line-handled, sprint ready, tech_debt_

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See https://github.com/flutter/genui/pull/812, which was later re-introduced (https://github.com/flutter/genui/issues/816#issuecomment-4094184175).

We could/should do one of the following

1) update the flutter org's allowlist to permit any version of subosito/flutter-action using a wildcard (if we trust it enough--I've not investigated this)
2) stop dependabot from bumping this version (con: we never get any fixes/patches made to it)
3) just handle checking out flutter ourselves, avoiding dependency on subosito/flutter-action altogether (experimented with here: https://github.com/flutter/genui/pull/802/changes/77b9d351abb712ea5e7fcee21a4892562af86db3..a41db5aa98b9edaee21f83e2caf14b886854fdb1)