What problem does this address?

When a page is password protected a password form is displayed.
This form is difficult to style, e.g. using the CSS class .post-password-form.

What is your proposed solution?

We should convert this section to a block, so that it's possible to style it via theme.json
This block should not be added to the inserter - or if only when stying a password protected template as suggested in #70432