Hey BwsB,
We’d be happy to help out. Sounds like you’re specifically unable to send calendar invites using your iCloud.com email in the Calendar app only. Other emails within the native Calendar app and while using your iCloud.com account with other clients, work without issue.
If this is the case, can you test to see if you’re able to send a calendar invite for your iCloud.com address from the iCloud website? For help with doing so, please review: Invite people to a calendar event on iCloud.com - Apple Support
This will help us with isolating things a bit further. Next, just to double check that you’re using the correct steps, we’d suggest working through these steps here best equipped to assist:
Invite others to an event
You can invite people to an event you’ve scheduled.
1. Tap the event, then tap Edit near the top of the screen.
2. Tap Invitees.
3. Enter the names or email addresses of people you want to invite, or tap to select Contacts.
Note: For you to send a calendar invitation to a contact, they must have an email address. See Add and use contact information on iPhone.
4. When you’re finished, tap Done.
If you don’t want to be notified when someone declines a meeting, go to Settings > Calendar, then turn off Show Invitee Declines.
Note: With Microsoft Exchange and some other exchange servers, you can invite people to an event even if you’re not the one who scheduled it.
This is outlined in more detail here: Send invitations in Calendar on iPhone - Apple Support
If unable to invite people to a calendar event on iCloud.com or in the Calendar app with your iCloud.com email address, you’d be best supported by reaching out to Apple for more assistance on this matter. They can be reached using this link: Get Support
We hope this helps out.
Take care!