Follow up, I updated to the supplemental catalina update and I noticed that I could not revoke the accessibility permission for Alfred.
I was able to fix everything by manually resetting the permissions with the following:
tccutil reset Accessibility
sudo tccutil reset Accessibility
Laptop froze after the first command, after a reboot and running the second, everything is working again.
Both my clipboard manager + snippets are now working, so I'm pretty sure this isn't an Alfred bug, just macOS.