Not sure. There is probably a way to do it but haven’t really thought it through thoroughly. If I had to guess, I would think you could set up a new and clean profile the way you want it, then copy the profile folder it lives in, and then when you want to clone it just create a new profile the usual way and then replace the content with the stuff you copied.
Also not sure if that is sustainable – you’d basically be making copies of ‘old’ profile data and over time the browser will move on and change, and at some point the data you’re copying could be obsolete.
But, another idea might be to still create a clean profile and set up Brave Sync to send its Settings into a Sync chain. Then later, if you want to duplicate it, create your new profile and temporarily hook it onto the same Sync chain. Then remove it from that chain so each of them again becomes independent. I have not tested this but in my shallow mind it seems like it could work out pretty well, and be sustainable.