When I've picked up calves like that I take a temperature, look at the color of it's gums/eye pigment for anemia, listen to it's lungs and treat accordingly for pneumonia if it appears to be present. If the calf is relatively stable I will deworm with a good dewormer like ivermec plus. We have liver flukes around so I am cautious to be sure they are treated for them. I check stool and be sure it looks normal for the situation. If I have any concerns about parasite overload I'll run a fecal so I don't cause problems by deworming an overly wormy calf. I'll give probiotics and vitamin B complex per directions on the bottle/tube to help stabilize the gut and increase appetite. I'll have some small grain out like calf starter along with fine stem hay. Something easy to eat and a little easier to digest until it's up and going well. I keep the hay free choice and the grain measured so I can keep track of consumption a bit and it doesn't get too dry and undesirable. I don't try and push calves like this too hard at the start. Even when they are really skinny. Slow and steady seems to be better in the beginning. I also don't vaccinate them until they are stable and going strong. I try not to tax the system anymore than necessary while they are not well. Most vaccine papers state not to give to unhealthy animals anyways. I know it's common practice for vets to give them but I personally do not until the calf is going strong.
This is just what I do when I pick up calves like this. Hope you can get him turned around and going strong. It should pick up on eating as it gets healthier. Good luck! Keep us posted