create a Group Email connect

Currently, it is not possible to do that on an iOS device. With iOS 16, that will change.

For now, you can use this option: if you go to iCloud.com in your web browser and then choose contacts, you can also create a group there. At the bottom of the screen you'll see a "+" in the gray column. You can then create a group here.

I have no idea why this doesn't work for you and the option is grayed out. I just logged into my iCloud via Safari under iOS 15 and I can create a group without any problems.

The only thing I can think of about this is that you might be at the maximum number of contacts.

Limits for iCloud Contacts, Calendars, Reminders, Bookmarks, and Maps - Apple Support

Contacts

• Total number of contact cards: 50,000
• Maximum size of a contact card: 256KB
• Maximum size of a contact photo: 224KB
• Maximum size of a contact group: 256KB
• Maximum size of all contact cards:
  • Card text: 48MB
  • Card photos: 200MB