That's what I did. But even if consider my advice to be mostly "language agnostic", i.e. not about grammar and orthography, I am pretty sure the recurrent small errors and weird phrasings undermine my reputation as someone that could teach the reader something
If I'm reading a piece by an author whose 1st language is not English, I'll make adjustments in what I think mistakes say about them. Most readers will. And I'll be focusing on content and ideas and glossing over sentence details.
It can be even be a positive, "This is impressive writing for a non-native speaker..."
If, on the other hand, you are trying to pass yourself off as someone with the same command as a native speaker, I'll be turned off.
> I am pretty sure the recurrent small errors and weird phrasings undermine my reputation as someone that could teach the reader something
I'm living and working in London and English is not my native language. I'm doing lots of grammar and orthography mistakes every day. They really don't matter as long as I'm able to get my point across. That's all it matters. Even if someone was in the position to tell me that they don't trust me, I would leave BUT I would go somewhere else, I wouldn't go back to my home country.
Well maybe the above doesn't completely fit your case, I just wanted to share my 2 cents.
OS: I have been writing in my tech blog in English the past 5 years. Often times I'm catching my self reading my older posts and just can't stand them. They are awful. :D
That's probably sort of true, but that would only undermine your reputation with a minority of your readership. And over time your grammar/phrasings etc would improve.
You could speed it up by having an editor review your work and that way you can also have confidence your reputation isn't going to be undermined.
It doesn't necessarily have to cost money to get someone to offer a second pair of eyes. Could be a friend or interested party. You could add an attribution "Edited by <name>" so they get something out of it perhaps.
It's pretty common amongst webnovels, translations, and fanfiction for an editor to help out and get attributed.