Coming up on my year probation

As the title says, I am coming up on my year probation period. Over the last year, my supervisor has been giving me fairly good marks but has always commented on my writing style. I feel like I've significantly improved and I've been using tools to help make my writing in the context they are looking for at least that's what I believe. I've had other coworkers review my work And I get significantly less marks from them than I do from my supervisor.

Today I met with them and again they brought up my year probation and that I still need to improve my writing. Even though the last few months they have been complementing my writing. Today, though they commented and asked if I was born here, as in the United States. They were not born here, and English is not their first language, but it is mine. The supervisor has made other strange remarks like this and has made a bit of upsetting comments that I found to point out or pick out the fact that I am a woman. Including describing me as having mood swings which I clarified with them, and they said they didn't mean it as a bad thing. And they apologize because English isn't their first language. They have lived in the United States for over 30 years. They always like to pick on the fact that, I hold conversations and present myself well in conversations with external and internal parties, but my writing does not reflect the same message or writing style that they are looking for.

I have had no complaints from other coworkers outside of our group, and get complimented on and requested by others to help with their projects.

So now I'm a bit worried as it comes up on my probation that they will decide not to keep me on as a full-time employee because of this. Does anyone else have any similar experience? I know I can't record our conversations legally because California is a two-party consent state. I've been advised to at least write down the dates and the times of the conversation when the supervisor has made some of these strange comments. so I've been doing that.

Ps: excuse my writing I did talk to text and Siri doesn't always do a great job of translating 😝

ps ps: edited so people can have paragraphs :) and a few more details