Apple mail does not sync on IPhone. I also have an Ipad. There it does sync. Settings are the same. Since last update of apple mail..

OK "Apple Mail" fooled me.

Settings , Mail, Accounts, Tap on Outlook account

Turn off Mail

Do NOT save any copies in phone

Repeat for any Google

Restart the phone

In the above settings turn Mail back on in both accounts

Leave on or off the correct contacts calendar etc that you use

iphone Settings, [your name], iCloud, (show all) turn off iCloud mail, restart the iphone, then turn icloud mail back on.

Delete the accounts and after restarting the phone, add them back.

Great feedback, thanks.