Migration of data from late 2012 macOSCatalina version 10.15.7 to 2021 24" Big Sur mac

The USB port on the Time Capsule is not used to connect to a computer. It is used only to connect another USB hard drive for additional data storage purposes.

You will need a Thunderbolt to Ethernet adapter to connect the cable to one of the 3 LAN <--> Ethernet ports on the Time Capsule. You will need to determine whether your Mac has an Thunderbolt 2 port or a Thunderbolt 3 port, which is also known as a USB-C port. Examples:

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You are missing the most obvious method.. wifi on the Time Capsule.

Put the TC close to your new computer ... or visa versa if the TC is still in the network.. or just use your normal wifi setup (as long as it is AC and faster than 866Mbps)

Over fast wifi the speed of file transfer is very good.. as long as you stick to doing just migration. Not quite as fast as ethernet but the TC is not the fastest data storage by a long long way.

Connect to the TC via Finder just to make sure you can mount it on the new iMac.. then you can copy the files via migration assistant.. with the following proviso.. Migration Assistant is not very granular.. you pick user files or not.. this can be a problem if the disk in the new iMac is much smaller than the disk in the old one.. i.e. less than all your files and settings. You don't want to move apps as Big Sur will generally have new versions of most apps.

Interconnecting the two computers over network should also be possible.. in this case you would still use wifi on the new iMac since apple built the base model without ethernet.. but your old iMac should be plugged by ethernet to the wifi router .. that is important.. Then run migration assistant on the both computers and it will give you info on how to configure old computer as source and new computer as target.

Can't answer. I haven't tried it. I have transferred files using Migration Assistant from a Time Machine backup on a Time Capsule to a new Mac using a USB-C (Thunderbolt 3) to Ethernet adapter with no problems.

If you are asking about direct transfer from a Mac to another Mac, this would be out of the scope for the support forums for the Apple AirPort routers and Time Capsule, but another user might answer.

In theory, yes. But, I have not personally tried this to confirm, so best to wait for more answers / confirmation.