Rename underscore-prefixed methods and properties

Split out from the coding-standards cleanup (#147).

The `custom_metadata_manager` class uses a legacy pseudo-private convention of underscore-prefixed method and property names (e.g. `_validate_metadata_field()`, `_display_post_metadata_box()`, `$_non_post_types`). PSR-2 disallows this, and the cleanup PR suppresses `PSR2.Methods.MethodDeclaration.Underscore` and `PSR2.Classes.PropertyDeclaration.Underscore` for `custom_metadata.php` rather than renaming, because renaming is a breaking change: several of these methods are registered as hook callbacks by string, and the names are part of the class's public surface.

This issue tracks doing that rename properly in a dedicated PR — updating every definition, every `$this->_x` reference, and the hook-callback strings together, verified by the test suite — after which the two suppressions can be removed.

Start in custom_metadata.php by locating the custom_metadata_manager definitions, the $this->_ references, and hook-callback strings named in the issue. Update all definitions and references together, run the test suite, and confirm the PSR2 underscore suppressions can be removed without breaking callbacks or tests.

Written by the indexing model from the issue text.