Looks like Ace has TypeScript support:
https://cdnjs.cloudflare.com/ajax/libs/ace/1.2.3/mode-typescript.js
However when I edit a .ts file, I guess you try to use the extension to pull it in because there’s a 404 for this in the dev console:
https://cdnjs.cloudflare.com/ajax/libs/ace/1.2.3/mode-ts.js
It’s a bit naff they didn’t name these after the file extensions but maybe TypeScript editor support is only a simple mapping away!