"Not enough space on Time Machine/Capsule. Backup not completed" --

Apple never told folks about that the fact that when the Time Capsule is close to full......and you have a larger than normal amount of new data to back up.......that Time Machine cannot automatically delete enough of the old backups to make enough room for the new backup.

You have two options at this point:

If you don't need the old backups on the Time Capsule hard drive, use AirPort Utility to erase the hard drive and start over again with a new backup.

If you want to keep the old backups on the Time Capsule, use the Archive function in AirPort Utility to copy all of the data on the Time Capsule hard drive over to a USB drive e connected to the USB port on the Time Capsule. Then......erase the Time Capsule hard drive and start over again with a new backup and move forward.

Be sure that the USB drive has the same or larger capacity as the Time Capsule hard drive. That would mean that the USB drive likely needs to be at least 2 TB capacity and possibly 3 TB capacity.

You are looking in the wrong place. Apple has never removed AirPort Utility from the Mac operating system. If you have a Mac, AirPort Utility is on it.

Click on the Finder icon (the "smiley face" on the dock) > Open Applications > Open Utilities > Open AirPort Utility

or

Click on the Search icon (the magnifying glass at the very top of your Mac's screen, type in AirPort Utility and then press the Enter button on your Mac.

Nice work!