How to set callback to execute after all the tinyMCE editors have been initialized?

You can wait for the specific editor manager to get added and then bind the init event handler to set content of the editor like this:

tinymce.on( 'addeditor', e => {
    if ( e.editor.id === <your_editor_id> ) {
        e.editor.on( 'init', event => {
            event.target.setContent( <your_editor_content> );
        });
    }
}, true );