Question about Property Taxes

X-post from r/Austin since they group all their real estate posts into a sticky and property tax structure is the same across the state.

I'm trying to help my mom purchase a home in the "Austin Metro Area".

Anyways, the problem is I'll have to purchase the home and she'll have to pay me for it due to credit issues so I won't be able to claim a Homestead Exemption since I have a house.

The question is, can I basically expect the tax appraisal for next year to come back as the purchase price? The reason I ask is because the difference is absolutely insane. Check out this house: 2159 Redwing Way, Round Rock, TX 78664 , listed for $327,000 . For 2021 it appraised at $200K. The difference is $125k+ almost double.

Obviously this makes a huge difference in what I am budgeting for property taxes, but it almost doesn't make sense for the appraisal to come back that high for next year. Wouldn't that mean that all the houses around there would also have an increase in appraisal, of course capped at 10% for homesteads but still, wouldn't this likely force people out of their homes? I doubt the average family who assumed they could pay $4500 a year ($325 a month) in property taxes could pay $9000 ($725 a month).