refactor: Migrate DataFrame display to use IPython's _repr_mimebundle_() protocol for anywidget mode

[shuoweil]

This PR refactors the DataFrame display system to properly implement IPython's repr_mimebundle() protocol for anywidget mode, moving widget handling logic out of repr_html() and into the appropriate display method.

See design doc here: screen/8XWbJDa2d9mb6r5

Fixes #<458796812> 🦕

[review-notebook-app[bot]]

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[tswast]

e2e failures

FAILED tests/system/large/functions/test_remote_function.py::test_remote_function_max_instances[set-None]
FAILED tests/system/large/functions/test_remote_function.py::test_remote_function_max_instances[no-set]

These appear to be unrelated.