Got a new Macbook Pro, now my AirPort Time Capsule isn't available for backup

I recently replaced my 11 year old MacBook Pro with a new one (hooray!) but want to keep using my existing AirPort Time Capsule to backup the new computer. I used the Migration Assistant to transfer all files etc over from my old laptop, then turned off the old computer. Now when my new computer tries to backup using the Time Capsule, i receive an error message saying the backup disk isn't available. All devices are on the same wifi network and all have been restarted; the Time Capsule appears in the 'Time Machine' app as a backup disk, but when I try to actually do the backup I get the error message. The Time Capsule currently shows as having 215 GB available.

Do I need to remove the Time Capsule as a backup disk option on the old computer in order for the new computer to be able to use it? Do I need to delete most of the old laptop's backups on the Time Capsule, and if so, how?

Thanks in advance for any advice!