Answer
Deleting only the Gmail service doesn’t delete the entire Google account, and by that NOT the Youtube channel. And if it works, delete the entire Google account, on the Google account side ( not the Gmail side ), and for the channel, on the Youtube site.
How to Delete Gmail Account with Youtube Channel Permanently
How To Delete YouTube Channel permanently without deleting gmail account in Hindi
Does deleting Gmail Delete YouTube?
Deleting only the Gmail service doesn’t delete the entire Google account, and by that NOT the Youtube channel. And if it works, delete the entire Google account, on the Google account side ( not the Gmail side ), and for the channel, on the Youtube site.