Sometimes awesome things come in small sizes –
rapid_typing is an tiny little project for a speed typing test. It was developed back in 2017 and hasn't seen changes for a while, but is very nice and minimal, and easy to self host (assuming you don't disturb the older build dependencies too much!)
If you're looking to build a typing application and want a reference, this might not be a bad reference project to start, even if the codebase is a bit old. Old code doesn't mean bad code!