***NO_CI***
- remove dev dependency `prettier` from non-tool packages when possible and
update them to run vendored prettier for `check-format` and `format` scripts
- upgrade rest of packages to prettier v3
- run `rush format` for all rush packages
This is a follow-up to https://github.com/Azure/azure-sdk-for-js/pull/28127 to
move the rest of repo to prettier v3.
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