Training dog / cat situation

Do you have a counter you could put kitty food on, in like a laundry room or spare bathroom?
Or even get a cheap, sturdy card table from a 2nd hand shop that you could put somewhere.

Otherwise, I would pick a room for kitty litter and food and place the baby gate in the doorway.
Since I have a large dog, I raised the gate enough for cats to get under, but dog can't get under or over.

I'd make a "kitty room" one where the cats can only go in. My dogs are only allowed in the living room/kitchen/dining room, there's a door that seperate the living room to the hall/family room/bedrooms and they aren't allowed back there, but the cats are. We used a baby gate to teach them to stay in, and also just kept on them about staying in the main room. My cat eats his food in my bedroom, where the dogs can't get to it. One of my dogs when I first got her snuck abck a couple of times and ate his food, but I stopped that right away.

You may discover that catfood bowls are the least of your worries... our dogs head straight for the litter boxes (yuck!!!!) and partake when they come into the house, so we either cover the boxes, or they don't come in (but do have their own room and outdoors (Samoyeds... not exactly poodles!).

I do counter / table or other high pt ....

You have a few choices.

One find a small table that the dog can't get on or reach very well. Put the bowls of cat food/water there and push it far to the back.

Or you can stop free feeding the cats and put out their food at set times.

In our new house, the cat food is kept in the basement on a counter (all the pet food is kept there). Our lab is trained from the start that she cannot go over on that side of the basement at all - and it prevents her from getting into the cat litter box too.

She will stand there no matter what and watch you but will not step foot on the other side. Even when we are gone, we can trust her not to go over there.