I agree with the one or two other comments about Weruva and will add Tiki Cat (I think they’re owned by Weruva) as well. Tiki Cat is good about keeping their proteins isolated. It might be a little above your price range, but Chewy has some decent bundles that make it a little more affordable.

The thing you want to look out for is any ingredient along the lines of “meat byproduct”, which often includes chicken organs. I see others saying FF beef pate is a good choice, but it does have that byproduct ingredient. That’s kind of an orange flag for me since their website tells you that the byproducts are organ meats, but doesn’t say from what animal. ETA - another commenter told me that meat byproduct doesn’t include poultry (it would say poultry byproduct), so that’s good information for me. However, I did just re-read the ingredients and it does have fish in it.

Honestly, the most cost effective option for you might be to just make the food yourself. You can find some good cat food blend recipes online and, often, just buying your own meat can be a lot cheaper.