If you dig into how property tax is allocated, your tax will only go up if your house appreciates more than similar properties - which usually has something like redevelopment or other externality.

It is normally not a fixed percentage of your value, but simply "here's what the county/city paid this/next year, divided amongst the properties proportionate to the value."

Some, like sewer, etc, are per-property, but most are done via the above.

California is an outlier because of Prop-13 but that makes it usually better except when buying.

Side-effects of this can mean that development in your district can reduce your tax rate, depending on what kind of development and who lives there (as property tax is often mainly a school tax, a development for 55+ will bring in more tax payers but not increase the school burden noticeably).