Remove legacy gen_defaults analyze checks (#191629)

Related to https://github.com/flutter/flutter/issues/184950

This PR is to remove the legacy `gen-defaults-names` and
`gen-defaults-up-to-date` analyze checks from Flutter CI.

These checks validate `dev/tools/gen_defaults`, which has become legacy
and only targets the frozen SDK Material library under
`packages/flutter/lib/src/material`. Material development has moved to
the standalone `material_ui` packages in `flutter/packages`, and we
introduced new `gen_defaults` script in flutter/packages, so these check
for old script is not useful at all.

This PR also removes the now-unused helper methods and their test
coverage.

TODO: the old `gen_defaults` tool should eventually be deprecated and
removed.

## Pre-launch Checklist

- [x] I read the [Contributor Guide] and followed the process outlined
there for submitting PRs.
- [x] I read the [AI contribution guidelines] and understand my
responsibilities, or I am not using AI tools.
- [x] I read the [Tree Hygiene] wiki page, which explains my
responsibilities.
- [x] I read and followed the [Flutter Style Guide], including [Features
we expect every widget to implement].
- [x] I signed the [CLA].
- [x] I listed at least one issue that this PR fixes in the description
above.
- [x] I updated/added relevant documentation (doc comments with `///`).
- [x] I added new tests to check the change I am making, or this PR is
[test-exempt].
- [x] I followed the [breaking change policy] and added [Data Driven
Fixes] where supported.
- [x] All existing and new tests are passing.