Then if the deleted emails are still showing in the iOS app even after weeks and you are giving the app time to sync the server changes, and nothing showing in Show Operations, and the deleted emails are definitely not on the mail server end, then sounds like either an OS glitch or other resident app possibly interfering, or the account is possibly corrupted in the app in some way, or the app cache or data might have become corrupted and is not synching new server data.
So first “if you haven’t already tried” suggest to shutdown and power off your iPhone and then power back on incase it’s an OS glitch or other resident background program interfering.
Sometimes eg: optionally installed iOS firewall / security programs or optionally installed antivirus programs or vpns can interfere with mob app mail synching. So if you have anything like that optionally installed on your mobile “other than the default iOS stuff” then try completely disabling those to test incase of interference.
If power cycling your mobile makes no difference and you have no optionally installed programs like the above, then next suggest to go to Menu / Settings / Accounts and “remove and readd the account” incase its a corrupted account in the app.
If removing and readding the account still makes no difference, then suggest to next “uninstall and reinstall the iOS app” completely and reset up via the QR Export Mac desktop menu and see if that fixes it to rule out if it’s an app cache problem.
If resetting up the app as new via the QR Export Mac desktop option makes no difference, then try with “cell data only” and not wifi “if you haven’t already tried” to see if that makes any difference just to rule out if it’s a Wifi connection issue.
Or even try the app synching “using a different private or public Internet wifi connection outside your house” and see if that makes any difference.
iOS 26.3.1 (a)
Apart from the above try upgrading to the latest iOS 26.4 just officially out and see if that makes any difference if you haven’t already tried.