Register the options screen rows with the Settings API

render() built the two form tables by hand: every tr, th, label and the
Display Options heading were literal markup, and the row order lived in
the template rather than in the registration.

Each option key is now an add_settings_field() against one of two
add_settings_section() sections, drawn by do_settings_sections(), so core
owns the table markup and the label pairing. render() is down to the wrap,
settings_fields(), the sections and submit_button().

The select rows pass label_for. The two template rows do not: their
heading cell carries the allowed-variables list, which core would nest
inside a label element, so they supply their own label in the title.

The use_ajax hidden field moved next to settings_fields(). It is what
keeps the stored value pinned off when there is no page cache, and it is a
hidden input rather than a row, so it does not belong in a section.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01EcmNzkCYLCvub6vDBMgcdg

Author: lesterchan