Not easily, but what you can do (what I do when setting up/resetting a phone): Setup ST clean on one device. Then configure all the folders/shares you want to use on other devices.
Do a backup.
Copy that backup to other devices. Restore.
Of course, this would overwrite anything there, but it’s good for that initial setup, to get the devices/shares in.
Edit: Also check out Syncthing-Fork. Gives you finer control within folders, such as battery and network settings, rather than for ST as a whole.
Edit2: I keep a share on my primary machine (desktop that acts as my server) just for information like this. There are text files in there, one is “Syncthing Info” with Device names, ST identifiers, share names/identifiers, descriptions, etc. Since my phone has that share, I can easily access all that info, or even share that share with other devices.