New install Big Sur show two Volumes named ...Data & Update

High Sierra is not going to recognize things for Big Sur or Monterey as you would think it should. Use the option key to restart and your Big Sur volume should show to select.

First, here are the requirements for Big Sur:

https://support.apple.com/en-us/HT211238

A 2007 iMac is simply not compatible and cannot boot or run BS.

Second, yes , BS devides the drive into two volumes; the OS will be on a read only volume called Macintosh HD and the Data volume will contain your user and other files you will actually have read/write access to. If you can get it to work, it'll be a miracle.

Big Sur and later create several Utility volumes along with a System Volume and Data Volume.

Those are Preboot, VM, Recovery, and Update.

When you boot into another OS, you will see the Data volume mounted, and sometimes the Update volume.

So, there isn’t any problem.

Ahh, I see. Well, things still may not go smooth since Apple changed its filing system. Here is another resource if needed:

https://support.apple.com/en-us/HT204904