I made an extension which allows you to quickly launch a speedtest using speedtest.exe, Ookla's official cli app, from playnite.
To use, simply click the menu icon, go to extensions, then click on Run speedtest.
Due to powershell being weird (and me being lazy), as soon as the speedtest is complete, the window closes, so keep your eyes open during the test to see your speed. I may fix this in a future update.
I've also got a copy of speedtest.exe on windows path, I don't know if that's a requirement or not, but if so just download it from here and add to path.
(Also to use it you need to agree to Ookla's term of use, privacy policy, etc)
(PS: Ookla are the people behind speedtest.net, they're like the main people to go to for internet speed tests)