The portable builds are fully portable, the profile directory is inside the browser folder. It does not touch appdata at all.
Changes on top of the previous 125.0.2 build:
Aero fog is adjustable in settings, with normal intensity, half intensity, and off.
Theme changes like red tinted private window caption bar are able to be turned on/off in settings.
Native style elements are able to be turned on/off in settings.
Native style tooltips and bookmark menus can be disabled now with the same settings mentioned above
EventSetInformation dependency should be gone.
Separate default search engine for private mode option is available now.
Translations popup does not appear anymore. It is still unconfigurable outside of about:config.
Haven't tested on XP/Vista (extended kernel) nor have I stability tested.
Please let me know what bugs or issues you encounter with it.