Two resources which helped me improving my writing, when I was writing my thesis were "How to Write Mathematics" by Paul R. Halmos and "Mathematical Writing" by Donald E. Knuth et al. I would always start with Halmos to get into the spirit of perusing clear and precise communication. The "Bad/Better/OK" suggestions especially reminded me of the discussions in the lecture notes from Knuth et al. And at a third step a linter such as the proposed one is probably helpful, if something slips through.

I think these resources are essential for anyone who writes on any subject which at least involves definitions here and there.