Why not iTunes never show the list backups that was taken on same iPhone with different Apple Id's?

Here is the story, My iPhone 13 Pro is dead/never turned on. So, I plan to use my wife's iPhone 15 Pro Max to get some of my important files from iCloud Storage.

1. Open iTunes, Connect my wife's iPhone 15 Pro Max - Apple id (rj.****@***.com)
2. Use the encrypted backup option to back up the whole device.
3. The first backup was done at 11:14 AM average size is 100+ GB,and the status shows the Latest Backup: Today 11:14 AM to this computer
4. Erase the iPhone from the settings
5. Start as a new iPhone, log in with my Apple ID (vig***@***.com) to recover data.restored the data from iCloud over Wifi
6. Open iTunes, Connect the phone to PC, and I try to back up again using backup option to backup whole device without encryption.
7. The second backup was done at 03:59 PM average size is 30+GB, and the status shows the Latest Backup: Today 11:14 AM to this computer
8. Erase the iPhone from the settings
9. Start as a new iPhone, log in with my wife Apple id (rj.****@***.com) to recover data, this time i try restore the iPhone from first backup.
10. Here is the problem appears, iTunes never shows the first backup in the list.

When I tried to locate the the backup folder, I can see only one folder as below

Then I entered the folder, it had a lot of sub-folders and all folders contain encrypted files in two timings, which was proof that the first and second backups still exist, with two timings.

But in iTunes, it was showing only one backup that was second backup.

Now I have a problem with 😭 wife's phone, that I cannot restore the first backup.

Please help me from the nightmare, we have a lot of memories and important data that were not properly to the cloud. A lot of important data is missing.

Thanks in Advance