Favorites are not lost when you change your work environment, so I'm not sure what problem you've encountered?
Favorites are saved as part of the file itself. If you want to move Favorites from one file to another, you simply Save them from the Favorites palette flyout menu and Load them in the other file.
Given that, like attributes, they are stored within the file - I can see the logic of a consolidated attribute manager-like interface that allows for the transfer of all internal data from one file to another. (Favorites aren't attributes, but are an aggregation of existing attributes and tool settings - so AM would have to be renamed IMHO if it included Favorites.)
Something that behaves similarly is Project Info (File menu). All of those data fields, expandable by the user to as many as desired - primarily for use with autotext, can be saved or loaded from that interface.
Karl
One of the forum moderators
AC 27 USA and earlier • macOS Ventura 13.6.6, MacBook Pro M2 Max 12CPU/30GPU cores, 32GB