Hello. I have now tested this with versions 24.3, 25.3 and latest 28.2. All have this problem.
First I create a new file with c-x c-f. By default, it has coding system iso-latin-9-dos.
I change the coding system to utf-8 via the buffer's bottombar. Char "0" changes to "U".
Then I write "äöäöäö" and quit emacs.
When I rerun the emacs and open the text, the "öä" looks wrong and coding system is back at iso-latin-9-dos.
I use Total Commander's View to verify the file is ok. The file goes wrong only if I now save the buffer.
What helps is c-x ret r which asks the coding system -- I type utf-8.
Also helps when I add ";;; -*- coding: utf-8-dos; -*-" to the top of file. I will use this method as solution, but this is too advanced for regular users -- please check what is the problem.
Windows 11 Home, ver 22H2, installed 11.10.2022, HP Pavilion Gaming Desktop TG01-2xxx