Homestead exception

Hello, new to Texas here. I bought a house last year and I was not aware that on 2022 you could file homestead exception without waiting for next year. For some reason on tax records there is a 2021 appraisal for land, on 2022 an appraisal that is less of what I paid for the house and this year 2023 I got a 100% appraisal increase which is way more of what I paid for the house exceeding the price around 30k.

Couple of questions: 1. If I file a late homestead exception will the district ask me for the closing price or will they take the 2022 appraisal? ( I don’t know how they came up with this appraisal) 2. Will filing late homestead give me the 10% cap based on the 2022 appraisal or based the closing cost? Or will the 10% cap will only kick in on 2024? 3. Since 2022 appraisal is lower than my closing cost will I owe taxes if I file late homestead exception?

It’s a little confusing so I’m trying to understand how all this work. Thanks!