monaco-editor version: 0.13.1
I would be really happy if there was an option to programmatically select the Use Regex option.

There already is -
controller = editor.getContribution('editor.contrib.findController');
controller.toggleRegex();
Thanks @brijeshb42, you're a life saver!
I wish there was more documentation and more examples on Monaco's website.
Most helpful comment
There already is -