Noticed I was having this issue too. Found this thread. Decided to just try completely removing my Gmail account, the one that wasn’t syncing with the Mail App after the iOS 18 update.
I went into Settings — Mail App — Mail Accounts (it’s conveniently the very first thing at the top so easy to find) then selected the account that wasn’t syncing (Gmail, in my case) and then selected Delete Account. In the scary red lettering.
I was a little hesitant but went ahead and let it completely remove all the synced items from the account off of my iPhone. After a minute, it was removed so just went and re-added it and BOOM. Works like normal! No more issues.
(For reference, I use an iPhone 13 Pro with iOS 18)