So mine is working correctly now. I can't say for sure what fixed it but I'm thinking it may have had something to do with the following:
I just got this phone (14 Pro). When I was first asked to enter my password to purchase an app (as opposed to asking me to do the double side-click which is what it has always done before), I entered my password and then it asked me to verify a form of payment on my account. This was very odd to me as I'm part of an Apple Family and I've never needed to use to Head of Family's credit card for my purchases as I've always maintained my own credit on there.
After doing some research I found this was standard for a new phone. The system knows that this phone hasn't been used for purchases before (regardless of being signed in to my usual Apple account) so a form of payment must be verified again from the new phone, even if said credit card wasn't even the form of payment one intended to use for that purchase. So I had to contact the Head of Family who gave me the code he was getting on his device for me to enter on my end to verify form of payment. Once I did that, my purchase went through (using my own credit as usual) and since then it hasn't asked for my password again. Now it asks for the double side-click again the way it always used to. Hope this helps.