Noticed problem immediately after the last OS update
So was that Mojave?? How long ago was that?
since purchasing it in 2013
Does it happen to be the tall one or the flat model.. A1409 which is last N wireless? 2013 was the change over year.
Actually to get 6 years out of a Time Capsule (TC for short) is pretty good going and it really may well be due an update. Of course since Apple no longer make them you will need to figure out another alternative.
Have run disc first aid
This will not work on TC. It is a network drive. First aid in disk utility is only relevant to local disks.
Problems started in a major way at Sierra with enhanced security which Apple continues to do with each OS.
In Finder mount the TC disk.
Make sure you can see the sparse bundle for your computer.
If you have issues mounting the disk then Time Machine (TM for short) will have the same issue.
How much space do you have left on the TC drive?
This will show up in the Airport Utility on the disk tab.

Try using a verify by holding down the option key while you click the Time Machine icon.. it will show verify as an option.. if it is greyed out or doesn't work then next best step is to do a full factory reset of the TC and start over.
Power off the TC.. hold in reset button and power on again.. having another body to help makes it easier. You must not release the reset while you are powering on.. and keep holding it in for about 10sec. The front LED will start flashing rapidly.. if you missed it try again. Factory reset will not delete anything on the hard disk. It just removes settings on the TC which is necessary now and then.
Redo the setup of the TC from airport utility in your laptop. Do NOT use Apple recommended names.. start again with a new name which should be short, no spaces and pure alphanumerics. Password same rules but can be longer.
Once you complete the TC setup open the TM preferences and change the backup disk since it will have a new name and password. You might get a screen asking if this is to replace your current backup.. agree that it is replacement.
You will then see TM is going to do a full backup for the first time.. don't worry.. what happens is TM checks the disk for previous backups.. will find the existing backup.. verify it and continue if everything is good.
If it fails at that point the best thing to do is start over a fresh clean backup.
If you want to keep the old backup.. use the archive function you can see in the screenshot above to a USB disk (Mac OS HFS+ format) disk of equal size to the TC disk or larger. This will take several hours if it is large.. ie 1TB or more.
Then you can use the Erase function in the airport utility disk tab.. quick erase is fine.. to wipe the old backup and then you can start a fresh backup.