HELOC - would an appraisal raise original mortgage?

We are looking at a HELOC and after scouring this sub I still am confused - assuming we need an appraisal to determine current value, wouldn’t that raise our taxes and original mortgage payments?

Not sure if this info is needed but purchased around $615k, still owe $550k, value is $675k according to Redfin which I’m sure isn’t super accurate?

We are first time homeowners and to be totally honest I read about peoples taxes and monthly payments increasing and that has never happened to us in the years that we have owned, and I don’t know why (/confession). I think when we bought it was appraised at 620k so it hasn’t gone up that much and honestly could be lower than Redfin says, but I’m so so so early into researching and understanding HELOCs and HELs that I’m trying to take it one step at a time and I’m stuck on how this could affect our current payments.