OK, thanks for the details.
Time Machine detected that your backup file on the Time Capsule was corrupted and tried to delete your old backup file......(the thing with with the long name).......and start over again with a new complete backup of your Mac. But, as the second message indicates, Time Machine could not delete the old backup file, so a new backup file to hold the new future backups could not be created or established.
All that you can really do at this point is try to manually delete the files on the Time Capsule by manually erasing the Time Capsule hard drive. Unfortunately, when you do this....and if it is successful.....everything on the Time Capsule hard drive is erased, including backups of other Macs that might also be backing up to the Time Capsule.
Once the Time Capsule drive has been erased, then you can try to run a new backup of the Mac. Unfortunately, there are no guarantees here that everything will run smoothly going forward. If the Time Capsule is 5-6 years old, for example, the hard drive inside the Time Capsule might be starting to fail. If the Time Capsule is 7+ years old, then it is probably better to stop using the Time Capsule and go with another backup plan.
So, the big question here is.......
Do you want to try to manually erase the Time Capsule hard drive.......which if successful will delete everything that is on the Time Capsule hard drive? Once that is done, you can then try to run a new Time Machine backup.......which will copy everything on the Mac over to the Time Capsule's hard drive and then move forward with incremental backups.
If yes......and you need step-by-step instructions to erase the Time Capsule's hard drive.......please post back to let us know. Once again, I need to stress that there are no guarantees here, so we are really at the "last resort" stage.