OSBLADE Does anyone know if Keeper Password Manager works with GrapheneOS?
Most likely, yes. Numerous other password manager apps are known to work on GrapheneOS: Bitwarden, Keepass, Proton, etc. There is nothing special about password manager apps (in general) that would make them unlikely to work.
Many people new to GrapheneOS seem to be more worried about app compatibility than they need to be. The vast majority of apps will work just fine. The main exception to that is banking and other financial services apps. Compatibility is actually a high priority for the project.
If you are interested in GrapheneOS, presumably security and privacy are important to you. Rather than asking, "Will app X work on GrapheneOS?" I think a better question would be, "If app X doesn't work on GrapheneOS, what alternatives do I have?"