It's about 6 years old
That was the change over year.. so is it tall one.. looks like this.

Or the previous model which is small pizza box shaped.
BTW the tall one is Gen5 and the previous one is Gen4. I presume you have Gen5 because it is totally lacking in model number.
It's going through the process of "preparing for backup", but then tells me I don't have enough room, which is not the case.
How much free space do you have?
It will show you in Time Machine.
How big is the backup supposed to be?
How much data total do you have on the drive/s Time Machine is backing up?
Time Machine may need to delete the existing backup and start over.. this can exceed the free space.
Do other computers use the TC for backups? Or are you storing files on it?
Let me suggest a few ways ahead.
Hold down the Option key and select the Time Machine icon.. select verify and it should then check the current backup.
Depending on the results of the verify, formatting the drive of the TC is probably the best fix.
If you wish to keep the old backup, use archive in the Disk tab. You will need a Mac formatted USB drive plugged into the TC of equal capacity or greater to the data/disk capacity.. ie 2TB or 3TB.

Then use erase. Since the TC is now 6 years old I would do a full erase. This is zero out data. It will run a low level format of the disk which ensures all the sectors are readable. This will take a few hours.

Once completed do a backup.. it will generally work on a clean disk.
TM is becoming less and less reliable with each version of Mac OS .. especially since Sierra where the rot really set in.
I strongly recommend an alternative like Carbon Copy Cloner.
If you want to run TM use it to a local disk plugged directly to your computer.
BTW 6 years is a long long time for Time Capsule to survive. It is actually time to look at replacement. Apple of course no longer make them so it will mean buying other brands. Please ask if you consider this for recommendations of what to buy.