In Credential Manager, I see that both Windows and Certificate-Based credentials are showing as disabled. I have gone through all of the group policies applied to the machine and haven't found anything that would cause that. I can't even find a way to enable that using a group policy. Does anyone know where that setting might be locally on the machine, or somewhere in a group policy where I haven't found?

I suggest you temporary disable the anti-virus and firewall. Then check the result. If the issue persists, please check related policy settings. Please open gpedit.msc, and find the following policy. Security Settings\Local Policies\Security Options\Network access: Do not allow storage of passwords and credentials for network authentication Please ensure that this policy is disabled.Arthur Xie - MSFT

That solved the issue for me too. Thanks!