Is it worth protesting property taxes?

I bought my house in Sep 22' for 520k. The property tax from the years before showed it valued at 305k, 345k and then 398k for 2021. Then, right into 2023, four months after moving in, we got notified it was now appraised at 450k. For 2024 they just pushed it to 500k (498k really).

I have homestead and a disabled vet exemption but I never noticed any drop. It actually went up after I got those two exemptions.

So my question is: Would it be worth it to try to protest and, say, request it to be lowered back to what it was before?

We've made zero improvements. The house already has signs of poor craftsmanship/renovation when we moved in. Things like new vinyl floors that are terribly uneven, poor paint jobs, drywall repairs that are super obvious, mismatched paint on the repairs, weathered and breaking material on window frames, sticking front door, bugs that come through old screens, all curtains and blinds removed, ants coming through poor caulking in bathrooms, damp AC with a mildew odor (plus some mold showing on the vents), leaky sink in bathroom and kitchen, sagging kitchen cabinets….you get the idea.

It took everything we had to get into this house, including life insurance money, and here we are getting mail saying "Good news! Your property has gone up over 46% from 2019 to 2024!". This is the smallest house in the neighborhood btw.

Again, given the details and backstory, would it be worth it to protest? Does the county see this and go 'this property used to be valued under 350 but this guy bought it for 520k, let's increase it to that over the next few years and make him pay?'

Long rant, I know, but any help would be appreciated.