To use the premium LanguageTool, you need to change some settings on the plugin. First you have to change the URL to https://api.languagetoolplus.com/v2/check, and provide your username and API key that you get from your personal settings here.

The settings should look something like this

If you type fast, there might be some words that get marked erroneously because the software does not clear the markings when you finished typing. If I got time on the weekend, I will work on a solution. In the meanwhile, reloading the note (opening another and then click back on the note) will clear the markings and only the real errors will be marked.