I think I found the reason for the incorrect voice search. In maps, as I wrote after a factory data reset, the operation was correct, i.e. the system language is used. In the Google application as well. The problem remained in the Google Play Store. While browsing Google settings, I looked into Speech Recognition & Synthesis. In the downloaded offline languages, there is only English (US) and you can't download any other language, like on my phone. I decided to update the Speech Recognition & Synthesis application and after that, the Google Maps search in PIP was again in English. Then I uninstalled all Speech Recognition updates and I am again happy with searching in the default system language, even in the Google Play Store. Try it on your own and let me know. I did not install Google Assistant at all, after testing I only added Gemini.
I think, that deeveloper should delete pre-installed English (US) offline language - this will be solution for everyone.