Problems restoring from time capsule

Replaced HDD with SSD.

Do you still have the HDD.. if so you win!!

Get a suitable USB enclosure and plug it into the computer.. migration can work directly from HDD.

OR

Assuming the disk was OK and this was done for speed.. you should be able to boot from HDD.. although this is removed from later mac with T2 chip I think.. a real pain as booting from USB is a huge benefit. Hold down option key at chime and choose USB for boot.. you are then back to your old install and can clone it to the SSD in the Mac if you want.. depending on how well the computer runs Big Sur.

You are not the first with Big Sur to have this issue. It does seem to have issues.

What OS was the computer running before upgrading the drive?

Do you have a computer running the older OS or can lay your hands on one?

Big Sur on the current computer should also work. Get a USB Mac format drive of size equal or greater than the TC internal (2TB mostly.. some 3TB) Plug it into the TC USB port. Make sure the TC sees the full drive size.

Use the Archive function in the Airport Utility.. this will transfer a clone of the current backups.. takes a day or so.. so expect slow.

Once complete disconnect the USB drive.

Plug the USB directly into the computer and use that as source of Mac backup rather than TC.. tends to work better and much faster.

The "password" could be.......

The WiFi or network password......if you set up the Time Capsule to use only one password

The Base Station or device password.....if you set up separate Base Station and WiFi passwords

The Disk password......if you set up a separate password for the hard drive

If Apple had you perform a Hard Reset, then you set up the password options when you set up the Time Capsule again.

However......IF.....you used the option to "encrypt" the backups when you originally set up Time Machine, then you set up a separate "encryption" password at that time. You must use that password if you encrypted the backups. Otherwise, things will get hung up at the "Transfer information screen"......and you will not be notified that the password was incorrect.

If you did not encrypt the backups originally, then unfortunately I have no other suggestions for you other than what Apple has already provided to you.