Hi and welcome!
I had 2 house cats before Pearl came home. I invested in a stair gate so the cats had a safe area (upstairs) and started to feed them upstairs before she came home.... Cat food is the second most prized food for dogs - the highest prized food is the output from cats

the litter tray also moved upstairs....
I also did the damp flannel trick: rubbing the cats with the flannel, then the pup before she came into the house and again the cats with the same flannel - especially down their flanks and if you can, either side of their faces. One cat took to Pearl immediately teaching her all sorts of cat play skills and tried to teach her to use the litter tray

thank goodness she was too big for the flap

.
The other cat didn't react so well - very highly strung 9 year old oriental. Over time he came round and was the only cat Pearl would let in the basket with her! Sadly Harvey is no longer here and much as Pearl and Minnie get on, still, she's not allowed in the basket

nor is the new cat!
Cats like routine and get distressed when it's changed - might be an idea to move their food now (if it's not already "dog safe") and their tray

Good luck with your new boy
Have you chosen a name?
Jayne and Pearl (blue roan age 3)