Import or replace Keychain entries from old Keychain files?

Name it whatever you wish just so it's not "login.keychain-db". Suggest something like "recovered.keychain-db". You don't want to conflict with the new Mac's default login keychain.

On your Synology turn on the built-in Time Machine capability and connect the new Mac to it. Then you can literally forget about backups. Leave it on overnight. The backup should complete. Then it will backup the changes every hour.

How much you work has little to do with performing backups. When catastrophe strikes, you will have all the time in the world to regret not backing up.

Technical logical troubleshooting is extremely difficult. I can't blame an Apple Genius or AppleCare phone support. As you just discovered, one little detail such as the usernames being different is likely the root cause of all the trouble. Even I didn't come to the conclusion until going through a whole slew of back and forth. Hands on is usually easier but someone still might not spot something like that the first go around. I made the assumption your username was the same.

I cannot count the number of times I banged my head against the wall till the wee hours of the morning completely exhausted, sometimes for days. Then it turned out to be something silly like a bad DNS configuration, a certificate problem, a typo on a saved hostname / username, file permissions that were incorrect, a faulty power supply, a bad stick of RAM, etc. Many times walking away, clearing your head, or taking a shower and then inspiration strikes. You return with fresh eyes and start from scratch and check everything then try that new angle that hit you like a bolt of lightning. Suddenly, you've fixed the problem. That rush you get when that happens is why I have been doing what I do for 30 years.

Many times, I'll walk up to assist a coworker, look over their shoulder and spot something that was staring them in the face for over an hour and they missed it. Sometimes you are just too close to the problem or you've waded too deep into the issue to see clearly. It is human nature, it's how our brains are wired.

The file you require is in /Users/<username>/Library/Keychains on the old Mac and is named login.keychain-db (login.keychain is the older naming) copy that file to your Desktop on the new Mac. Rename the file then move it to the ~/LibraryKeychains folder. Use the newer file naming convention. Then open Keychain Access and click on File -> Add Keychain and point to the file on the Desktop. Enter the password from your old Mac when prompted.

On the sidebar you will see the additional login keychain listed. Copy the passwords and other entries you need to the new login keychain. Alternatively you can click File -> Import to import everything but I think the concept of only importing what you need is advantageous.

Highly recommend you at least setup a Time Machine backup for the new Mac. It's ridiculously easy to do. Just buy an external disk that is double or more the capacity of your internal disk. When you plug it in, macOS will ask you to make it a Time Machine drive. Doing so turns it on and it will perform a full backup to the external disk and then backup every hour on the hour. When disconnected, it will snapshot to the internal disk and when the disk is attached, it will backup the snapshots to the drive. There is really no excuse to not backup when it's such a no-brainer and super easy. There's other backup methods such as Carbon Copy Cloner / SuperDuper and online cloud backup services such as Backblaze. Or you can save files on iCloud, Google Drive, OneDrive, Dropbox, etc.

Highlight the keychain on the left side and right-click it. Unlock the Keychain using the password you used on the old Mac. Then it should work when you drag and drop.

I don't think you can move items to iCloud keychain.

As Miracle Max would say, it was merely mostly dead but not dead entirely.

Is your username the same?