iPhone Mail log in problem

You csn Backup, restore to factory, maybe set up without restoring the backup and test Mail at that point,, then restore from the backup:-

(If the phone ever needs attention you will have to do this anyway)

If you can import your media to Photos or iTunes in a computer and copy important documents to a cloud server it will give you some resilience in case the restore from backup fails, or you need to ditch the backup and start as new. 

See here for the resources you need. Allow a couple of hours:

(1)          How to back up your iPhone, iPad, and iPod touch - Apple Support

(2)          Restore your iPhone, iPad, or iPod to factory settings - Apple Support

(3)          Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

If the problem remains then do step (2) again but set up as new without restoring any backup.

 If it fixes it then it is probably a rogue app or setting.

Possibly you have Two Step Verification turned on in the Google Account. Check with Google support or web search how to to that, ie what password to use in Mail app

I suggest this link but cannot verify its authenticity

https://apple.stackexchange.com/questions/142040/how-to-connect-ios-mail-app-to-gmail-with-two-step-verification

The email address was found, so that is not the probem.

It cannot get to asking for password so password is not the problem.

I don't know what the problem is unless you have a management on the phone by a company or school.

Turn off Screen Time

Force restart the phone

If that does not work you will need to do something drastic like restoring the phone to factory settings and trying again.

Back up first

Is it spelled correctly?

Please don't keep posting your email addresses

If you want to backup to iCloud you will need to buy the 50GB package. 2.5GB is no good

If you delete anything from iCloud it is generally gone forever

ok so that's not a problem