feat: re-land cache update patch

[felangel]

Re-land #1958 which was reverted in #1975.

Also ideally complete #1976 as part of this work to prevent future regressions.

[felangel]

FYI @bryanoltman

[eseidel]

There have been a few cache-related issues of late:

1. This one (pre-caching)
2. Installing only one version of Flutter on CI (instead of both the latest as well as the one the user requests with flutter-version in our GHA) feat: Specify flutter version and/or disable automatic download setup-shorebird#18. Also feat: precache flutter during shorebird install install#33
3. Making shorebird update actually do the full upgrade (without requiring a second run of shorebird). flutter knows how to do this, we'd just need to look and see. feat: shorebird upgrade should compile shorebird #289 feat: shorebird upgrade should print the new version number. #288
4. Cache artifact validation (we don't currently check in or confirm hashes for downloaded artifacts, which means that sometimes they don't survive the download/extraction, e.g. bundletool. fix: bundletool.jar download is sometimes corrupt (need to verify artifacts) updater#175

[eseidel]

Some subset of those might be something someone could take on when they're next paged-in on our caching logic.