I am working on a hobby project which tends to help the non-native speakers figure out if the sentences they write are good enough and sounds like written by English native speakers. Any relevant info are appreciated!
It seems that you're looking for what's commonly called "learner corpus", i.e. data that's written by people of various skill who don't speak the target language natively but are at various proficiency levels of learning it.
There are many such resources for English, the largest of which seems to be the Cambridge Learner Corpus, however, it looks like it's not openly available. Perhaps using it through an intermediary service such as https://www.sketchengine.eu/cambridge-learner-corpus/ is sufficient, or alternatively you might be able to find other learner corpora.