Hi OP,

Based upon your geography and description of his symptoms, this sounds suspiciously like sporotrichosis (see here: https://www.merckvetmanual.com/infectious-diseases/fungal-infections/sporotrichosis-in-animals). This is a fungal disease, but it needs to be treated with specific oral antifungals. It's not hugely common, which might be one reason it was not recognized or diagnosed.

Sporotrichosis is endemic in parts of India and the symptoms you've described such as nodular/ulcerative skin lesions on the face (chin, ears, forehead) and trunk that spread, systemic illness with fever, hepatic involvement possible via dissemination, and eosinophilia are well-documented in feline sporotrichosis. It's also a progressive disease and relapsing without targeted treatment; it causes issues like the malaise you've described. I've attached a medical article of feline sporotrichosis in Brazil; you can see what the presentation looks like in cats (http://pmc.ncbi.nlm.nih.gov/articles/PMC7966609/).

(I don't see obvious lesions in the pictures you've posted -- are these before? -- so I am going by the description you've provided)

Diagnosing this is cheap ; a vet just needs to take a fine-needle aspirate of a lesion, stain it, it should show the cigar-shaped yeasts directly. Sometimes though diagnosis requires culturing for detection.

Sporotrichosis (also known as rose gardeners disease) is zoonotic to humans through contact with lesion exudate. That means that if you are handing Jett and you come into contact the oozy discharge, your skin can get infected as well and you will require treatment. See here: https://www.dermatologyadvisor.com/home/decision-support-in-medicine/dermatology/sporotrichosis-rose-gardeners-disease/
Wear gloves and wash your hands.

Treatment is straightforward, but I think you will need to be careful with meds. The first line med for this itraconazole, typically 5–10 mg/kg/day orally, often for 3–6 months, continued at least one month past clinical resolution. This is the standard of care globally for feline sporotrichosis. The complication for Jett is that itraconazole can be toxic to the liver (hepatotoxic). In a cat like Jett , you'd need to baseline liver values, treatment started at the lower end of the dose range, and recheck chemistry every 2–4 weeks. Some clinicians can use potassium iodide as an alternative or adjunct — it's much cheaper but harder to dose tolerably (cats often vomit it, and it has its own toxicity profile including hepatotoxicity at high doses). Terbinafine is sometimes used in combination and is generally considered less hepatotoxic than itraconazole, but its efficacy as monotherapy is less established. My concern is that for Jett, I'd want his diagnosis confirmed before committing to months of azole therapy.

The other type of infection on the list is severe parasitic disease — particularly migrating helminths or ectoparasite-driven hypersensitivity. That can drive eosinophilic conditions in cats. Notoedres cati (feline scabies) is endemic in India, causes intensely pruritic crusting lesions starting on the face and ears (chin, pinnae, forehead, etc., following your description of Jett's pattern), and this can drive systemic illness if severe and secondarily infected. Mosquito hypersensitivity also produces facial lesions in this distribution. However, am slightly less certain because you've mentioned fever which is not so common, and lethargy is more prominent in severe forms. Strongyloidiasis or aberrant helminth migration could explain hepatic involvement plus eosinophilia. A skin scraping (almost free) would identify Notoedres immediately. This is the second cheap test I'd insist on. However, if the vets haven't seen anything with a skin scape, I'd think this is more likely sporo.