BUG: Fix to_html adding time to datetime columns in transposed DataFrame (GH#10640)

[epabarker]

• Closes When transposing a datetime index without time and using to_html, time is added to column titles. #10640

Description:
When using to_html on a transposed DataFrame with a DatetimeIndex, the column headers were including the time component (e.g., 00:00:00) even when it should be hidden. This was because HTMLFormatter was using the raw column values instead of the formatted values.

Fix:

• Updated HTMLFormatter._get_columns_formatted_values to use self.columns._format_flat(include_name=False), aligning the behavior with NotebookFormatter and respecting display options.

Verification:

• Added regression test test_to_html_datetime_columns_no_time in pandas/tests/io/formats/test_to_html.py.
• Added release note in doc/source/whatsnew/v3.0.0.rst.

[github-actions]

This pull request is stale because it has been open for thirty days with no activity. Please update and respond to this comment if you're still interested in working on this.

[mroeschke]

Thanks for the pull request, but it appears to have gone stale. If interested in continuing, please merge in the main branch, address any review comments and/or failing tests, and we can reopen.