Something similar has been happening to me for a couple of months on Big Sur (there is a thread about it around here somewhere where other people were reporting the same issue). I’ll have an app, which usually seems to be Day One, but it has happened with other apps as well, where it won’t install. The difference for me is that they look like they download, but when they get to 100% installed, they go back to the update available status. It always clears itself up after a week or so, so I never worry about it. Never figured out how to force it though.
So I am no help, but other people are having similar issues.