I believe this phenomenon is called “linguistic relativity”, or “The Sapir–Whorf hypothesis” [1], which says that a language affects its speakers' cognition or even personality. I'm probably not truly bilingual, my native lanuguage is Ukrainian, but I too feel as if my personality and behavior is slightly different when I talk or write in English.

Further reading:

1 // https://en.wikipedia.org/wiki/Linguistic_relativity

https://qz.com/925630/feel-more-fun-in-french-your-personali...

Chen et al 2010, https://journals.sagepub.com/doi/pdf/10.1177/014616721038536...

Chen et al 2013, https://onlinelibrary.wiley.com/doi/abs/10.1111/jopy.12040

Athanasopoulos et al 2020, https://www.tandfonline.com/doi/abs/10.1080/02643294.2020.17...

M. Keith Chen 2012, https://elischolar.library.yale.edu/cgi/viewcontent.cgi?arti...

I'm bilingual portuguese/english, and two completely different personalities. I have a really hard time flirting in english, for instance, when in portuguese it's very easy. Also I always write perfectly in portuguese very rarely mispelling a word, whereas I'm a full blown dislexic in english. I think it only shows how much language is the code of learning.. I learned to read and write both in E|P at the same time, and spoke english daily for 2 years as a child in Africa, but after that I went back to speaking only portuguese in Brazil, and having english mostly for the sole purpose of entertainment. Another notable differences I could notice is that with English I have a much more flexible accent, which can easily vary after spending a few days speaking it on travels.

I was told I had a different personality in English by fellow Japanese learners. I think it’s sort of common.