Any costs, including loan acquisition costs and closing costs, on a refinance are not home acquisition debt.

https://www.irs.gov/publications/p936#en_US_2020_publink1000229994

The calculation for the amount of home acquisition debt in the new loan is equal to the home acquisition debt principal that was paid off with the new loan.

(If a portion of the new loan is used for additional home acquisition, that would add to the balance.)

Admittedly, this is only from an IRS pub--I have not researched for stronger authority.