It sounds like you restored your new iPhone 12 using a 14/07/2025 backup, but your Messages only go back to May 8th. Everything else restored correctly, which suggests the issue is specific to Messages.
If you had Messages in iCloud turned on with your old phone, your messages wouldn’t be part of the backup—they sync separately. Go to Settings → [Your Name] → iCloud → Messages and make sure it's turned on. Then leave your phone connected to Wi-Fi and power—it can take several hours or longer to re-download all messages.
If iCloud Messages was turned off, then your messages should’ve been included in the backup. However, sometimes backups don’t capture the entire message history, especially if the backup was interrupted, the phone had low storage, or the Messages app wasn't fully synced at the time.
Since Apple Support couldn't retrieve them, it likely means the messages weren’t fully saved in iCloud or the backup. Check if you have another device (like a Mac or older iPhone) that might still show the missing messages.
Also, visit iCloud.com to see if Messages are available there (only for some accounts). If they’re still visible on another device, you may be able to force sync them back to your new iPhone.
Unfortunately, if the messages weren’t synced or backed up, there’s no way to recover them.