Firstly, click Show All Devices in the Disk Utility window to make sure you have viewed all drives and select the right HD. If the drive still shows uninitialized and reads Not Supported in Partition Map, I suggest you erase the drive and perform the restoration task one more time.
Both restoring from Time Machine Backup or local APFS snapshot work fine. The former needs sorts of downloads and installation work while it is a more common backup method.
Step 1: Erase Macintosh HD on your Mac.
1. Boot Mac into macOS Recovery Mode.
2. Get into Disk Utility.
3. Select Macintosh HD in Disk Utility.
4. Specify a name and format. You'd better select GUID Partition Map and APFS format.
5. Quit Disk Utility and reinstall macOS.
Step 2: Restore from Time Machine backup or snapshot.
After the Macintosh HD erasure, you can restore your Mac from either a Time Machine backup drive or an APFS snapshot as you like. After the restoration, go to check the partition map of the hard drive and log in to your Apple ID one more time.
Hope this answer helps!