[material_ui] Migrate M3 BottomAppBar template to use new gen_defaults

[elliette]

Work towards flutter/flutter#187899
Fixes flutter/flutter#188403

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Test exemption: Template migration PR.

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[gemini-code-assist]

Code Review

This pull request refactors the generation of Material 3 defaults for the Bottom App Bar. It removes the inline _BottomAppBarDefaultsM3 class from bottom_app_bar.dart and replaces it with a generated part file (bottom_app_bar_defaults_m3.g.dart). Additionally, it introduces a new BottomAppBarTemplateM3 template class to handle the code generation and integrates it into the gen_defaults.dart tool, while removing the legacy BottomAppBarTemplate class. There are no review comments, and I have no feedback to provide.

[QuncCccccc]

LGTM!