Mac OS asking for permission to compose, delete, read gmails etc!

As far as I can tell, wording aside, this is as innocuous as can be. You added an e-mail account, presumably so that you can use it with your e-mail client program. You know that it is you. You want to be able to, say, press Command-Shift-N and have Mail download your new messages; or delete a message and have Mail talk to the IMAP server and do what needs to be done to fulfill your commands.

All you are being asked is: are you sure you want this?

If you were NOT asked this, and Gmail would just let you start using Mail you would not have been concerned. So why are you if it merely asking “are you sure” before doing what YOU asked for?

This is very simple, and very normal.

In order for Mail to access your gmail account, you have to give it permission.

That's just it.

I forgot to add: why you were not asked before? Security protocols change. It used to one needed only an account and password, but often now one is required more, for increased security. That is why we have 2-factor authentication. This is similar. I also had not been asked that question when creating accounts before, but now I am. Just like when replying here I sometimes have to type a security code sent to one my trusted devices.

Temporari mutantur et nos mutamur in ilis (my Latin is not great 😊)