Apply core/settings review feedback to the core/content ability

Re-applied on top of the current branch tip (a prior push of these changes was
overwritten by a force-push). Mirrors the core/settings review fixes that apply here:
- Memoize the exposed post types so the input schema and the permission/execute
  callbacks derive from a single walk of the registered post types.
- Default the input schema to an empty object so the type:object default serializes as {}.
- Use __() instead of esc_html__(), and @SInCE x.x.x per CONTRIBUTING.md.
- Harden input/value handling (type guards, capability resolver, non-negative int
  helper, dynamic-property annotation) so the new code passes PHPStan at level max.

The `content` ability-category fallback is kept on purpose: unlike `site`, `content`
is a new category not present on the plugin's minimum WordPress (7.0).

Author: jorgefilipecosta