One example the ORG used
After former US president Donald Trump imposed sanctions on the court over its arrest warrant for Israeli prime minister Benjamin Netanyahu, reports emerged that the email account of chief prosecutor Karim Khan was blocked. Microsoft denied cutting off access, but the ICC later confirmed that in October 2025 it had stopped using Microsoft services altogether, switching instead to openDesk, an open source European platform.
Stow cannot do this as far as I know. Chezmoi can though you'll need to fiddle with templates and ignores to achieve it:
https://www.chezmoi.io/user-guide/manage-machine-to-machine-differences/#handle-different-file-locations-on-different-systems-with-the-same-contents
However as others have said a dotfile manager may not be appropriate for all apps. It assumes a certain kind of behaviour of the app - known config locations, text files etc.
I think your suggestion to backup/clone/restore your ideal Firefox config onto new machines is probably most practical if you do want to use a dotfile manager with it. That way you ensure the dir name is the same across all machines. Then you can use stow to manage parts of the profile going forward.
I would consider FF's own sync solution also though - I believe you can self-host it too.