Syringe feeding is stressful for both guardian and cat, and not very effective. Most cats will fight you for every swallow. And you would be surprised and saddened by how many syringes a day you need to give to keep up with their needs. Call your vet. He can prescribe an appetite stimulant and anti-nausea medication (if needed.)
In the meantime, you can try to crumble up treats into his food. Or you can try some grocery store brand foods like Friskies or Sheba. Popular brands are popular with cats. They wouldn't be on the shelves otherwise. I normally recommend that fish be avoided. But exceptional times require exceptional measures. Restarting a sick cat's eating is the best reason to bust out the fish. My Krista would eat Tiki Cat tuna flavors when she had pancreatitis and was refusing everything else.
Your kitty is on baytril for an ear infection? But no meds for in the ear? (Or is it baytril otic?) Unusual to prescribe systemic antibiotics for an ear infection as the ears don’t readily respond to them bc the ears are kind of their own entity. They don’t easily absorb the systemic antibiotics. Was his appetite bad before the infection? Or is this the result of the vet’s visit and treatment. Either way, I would call your vet to let them know this. Syringe feeding him water in The mean time is ok if he doesn’t mind it. It’s important to keep him hydrated but obviously you know this. Also, you can try him on anything to eat, deli meat, tuna, anything, until you are able to contact the vet.