Contacts Migration, iCloud confusion

I am migrating from Android to iPhone and am confused about iCloud and Contacts.

This will be a detailed narrartive. Where did I go wrong? What am I looking at? Where are my Contacts stored - in the could, or on the device? The Mac (latest Monterey) and the iPhone (very latest 15), do not appear to be in sync. I am also confused by the Contacts app on the iPhone, which seems to have changed (after my migration procedures, and post-upadte to latest patch level of iOS 15 which happened during the story).

I began by using the "Migrate to iOS" app on my Samsung phone, as directed from the iPhone the phone activation process. I do not know exactly what that did.

On the iPhone, I configured accounts so that contacts would come from Google. That seemed to work. HOWEVER, now I have changed my mind and decided to just migrate to iCloud and ditch the Google accounts.

A major goal is to be able to have Contacts groups on my iPhone. (Groups on the iPhone cannot reference contacts on the Google account.) I want to be able to make calls by using Groups to find the contact. Groups will be like "Family", "Medical", "Friends", "Dancers", etc.

I think those groups were proprietary to the Samsung phone, perhaps not even in the Google cloud. In any event, after all that, they don't show up in Contacts or anywhere on the iPhone. Looks like I will have to re-create them by hand.

On my Mac, the Contacts app looks like there are no iCloud contacts. Before and after the "move". This is as expected. Just the default "Apple" and my own vcard contacts in iCloud.

I used Contacts on my Mac to export all my Google contacts to a giant vcard file. Then I used System Preferences to remove Contacts access from the Google account. In the Contacts app (we're still on the Mac), the Google account disappeared. No more contacts. Good. Then I did Import, and all the contacts re-appeared as expected. All the information is there: their little photos, all the extra fields such as "Spouse", notes, etc. Everything is under "All Contacts", and everything looks good.

Now for the iPhone, and here's where the confusion begins!

I go into Settings and turn off Contacts for the Google account. (I don't think I had to do anything to turn on iCloud contacts; I don't think it's even possible to turn them off.) I figure it might take a minute to refresh, so I wait a few minutes, and power cycle the phone, and wait a few more minutes.

Now when I look in the Contacts app on the iPhone, I see all my contacts. I assume this is coming from iCloud?

There are two things wrong.

1. The contacts have their pictures, but the relations fields seem to be missing. The things like "Spouse" aren't there.Shipping address.

Maybe that's how things looked before, when they were coming from the Google account. But the info DOES (still) appear on the Mac.

2. I want to create Groups in Contacts. But I no longer see any buttons for that in the Contacts or dialing app. There used to be a "Groups" tab in the app - that seems to have vanished as well!

I am quite baffled. Don't know where my data is located (iCloud, device, both?), and why some of it appears on the Mac but is missing on the phone. Don't know why the iPhone app changed out from under me and the "Groups" feature has disappeared.

Very disconcerting, as the entire reason to move off Google was to be able to use the Groups in Contacts!

I still have my Google cloud and VCF dump, so I haven't lost my original data. But as far as the Apple ecosystem goes, things seem all bolixed up.

THANKS FOR ANY HELP!