As far as I know, Monzo only uses the Google API to identify & display merchant locations on the transaction details’ map.
I’m also pretty sure that they generally locate you by asking you to share your address so that they can send you your card. Although they can send your card to a different address in some circumstances.
Lastly you can switch on location based security to help prevent fraud & they use your location to spot when you go abroad. But I don’t think this is linked to Google’s services.