You might be able to do something with https://wiki.archlinux.org/title/XDG_Desktop_Portal - it was designed for applications running in flatpack and wayland to be able to get things from the system. As such I believe it lets you use a system file picker to be able to access files outside of flatpack. For applications that support it you might be able to get it to work outside of flatpack to get a consistent file picker.
Though I have not tried it and it may or may not function without wayland. Not sure if there is a way to do something similar in X11 otherwise. At least not without configuring every applications that supports multiple file pickers to force them to use one (like I think firefox can use the kde on if it is running on kde? or is that just theming on the gtk one...).