Based on Bowie's signs, I have to say that I am quite concerned by that breathing rate. At rest, it should be ~20-30bpm, so he is definitely showing elevation here. That raises concerns that we could have a oxygenation issue (ie heart,lung, blood level problems) but given everything else he is facing, I suspect it could be related to discomfort or even pain potentially due to constipation here. And that fits with the tightness you are feeling there (and thankfully he is passing urine; since that is an ER situation for cats when they cannot).
With this in mind, we need to tread with care. We don't want him to be breathing like that and uncomfortable. Therefore, to start, we can help relieve mild constipation but plan to have him seen if we cannot get things moving. In regards ***** ***** we can start by using some cow milk. This is because they are like little lactose intolerant people and therefore this can help move things down the gut a bit quicker. Or you can treat him with a dose of OTC cat hairball medication. This works to lubricate the gut and can facilitate the movement of hard feces out of the rectum. Alternatively, we could also mix a small volume of a GI lubricant (ie Miralax, lactulose, or food grade mineral oil) into his food. Do avoid giving it directly, since we’d want to avoid any aspiration risk.
Further to this, if he is eating you can mix in some fiber (ie a spoonful of canned pumpkin, all bran, or a 1/4 teaspoon of unflavored Metamucil) into his food. Just like people, these can restore fecal output regularity. When offering these, its best to use wet food both for ease of feeding but also since canned food is 35% water. It’s a good way to make sure we are getting fluids into him. As well, you also want to encourage him to drink by offering fresh water, low salt chicken broth, or even lactose free milk. The increase in fluids with avoid any dehydration risk, which can make constipation worse.
Overall, we need to tread with care if he is breathing so quickly (especially when not purring) and this belly is tight. The above can get feces moving in mild cases but if we aren't seeing stool in the next few hours, then we may need a double check with his vet and an enema.
Please take care,