Im not a medic, but have fair but of experience of this issue.
Do whatever you can do to get a Dietician involved.
GP/Dr should refer if he's lost more than a certain % of body weight over certain time. See NICE guidelines if needed.
There are special medical drinks that are especially high in calories AND vitamins & minerals. So even if only a small amount is drunk, the calories & protein & nutrients are in the body (& easily absorbed).
Fortisip COMPACT (extra protein variety if poss) or Ensure COMPACT are the extra-'strength' in a small size variants.
You can find them online while waiting for Dietician to get involved - they may well prescribe them. Up to 3 a day.
Should ideally also have a multivitamin & mineral. Best to get Dietician input on that given the medical history &/or current meds, because of possibilities of contra- indications or interactions.
Low iron / anaemia can cause breathlessness. Liquid form can be easier to absorb.
Again, Dietician input is best. Also iron supplements can cause constipation & thereby other issues, so best to be prepared to head that off.
Low level infection can also burn surprising amount of calories. If sorting the calorie intake doesn't stop the weight loss, consider asking for tests for inflammation markers to be repeated & focus on getting that under control (I see he's already on antibiotics, ask if they're having g the right effect & if not, review).
If there is difficulty getting a Dietician involved, could try hospitals PALS (patient liaison service) but that's for when normal channels aren't working.
Very sorry you are going through this. Wishing you all the best.