Update - I installed X now through Play Store after installing Play Store in Private Space. And I can logged in.
I think @GrapheneOS team should look into this issue.
An app installed from Play Store in Main Profile then installed to Private Space through "installed available apps" behaves differently than the same app installed through Play Store within Private Space.
Note - X users (including me) are getting LoginAttestation..... notification when logging in. The solution is to Forget password > then give the same or different pass > it will work. I logged in the same way.