Hi Abbie Y and welcome!
When you first bring the new guy home I would definitely give him time to get used to his new home. If it were me I would have him in a room where Carmello won’t be able to even get to at least until he’s comfortable with his new surroundings. Once he’s comfortable you can start prebonding, which is swapping their litter boxes, toys, dishes, etc. I think it’s very important to have them be able to see each other and interact from a safe distance when doing this process. It’s normally best if they can live side by side with a gap of at least 6″ between them but I understand that Carmello may spend some of her time throughout the rest of the house as well. My buck is free roam in his own room and I thought it would be okay if I set up my second bunny elsewhere and had them have play time next to each other along with swapping items. This didn’t work. I ended up having to set up a pen for my first bunny and had them live next to each other and swapped their pens every day before I tried bonding them again. It broke my heart to do this but I knew it was something I had to do. It helped greatly but sadly I lost my second bunny before they were able to be bonded.
For my second bonding I just couldn’t bring myself to move my buck out of his room again. I ended up moving my new doe into his room and had them share the room. My doe had a cage with a pen attached. While I was litter box training her she would spend the time I couldn’t watch her closed in her cage and during this time I would collapse the pen so my buck could use her area. I also swapped their items and I think both of these things helped do a similar thing to the pen swapping as far getting them used to each other’s scents and losing track of what they thought was theirs. I was shocked that through that whole time neither of them did any territorial marking. After doing this prebonding for a month I was able to successfully bond them in about 3 weeks. There were a couple of days of territorial marking during the bonding time but I was able to move them back into this same room with no territorial issues.
Honestly what you may have to do has a lot to do with how compatible they are. I can’t say that if I had followed the same process I used the second time it would have worked for the first pair since clearly they were a more difficult match from the start.
The other issue with bonding a free roam bunny is having neutral territory to bond them in. It’s actually best to have multiple places in mind because you may have to change things up. That was an issue I ran into because I didn’t have much to work with since my buck had been almost everywhere in my house.
In the bonding section I do have a topic about my second bonding experience and it ended up basically being a bonding journal if you wanted to see what I dealt with but I tend to be long winded.
Thank you for giving another bunny a home and good luck with them! It’s such a joy watching a bonded pair.