This is possible with the standard wp-editor by using the filter 'mce_external_plugins' then calling a custom plugin .js file. How can I do something similar with the wysiwyg field ?
The wysiwyg editor uses wp_editor() function to render the editor. So it might use the same hooks as the default editor (I'm not 100% sure about that, this need to be checked and confirmed). You can try disable Gutenberg first, since tinyMCE in Gutenberg is heavily customized and hooks might not work.