Sidecar with 2 different ICloud accounts?

Hi,

My wife and I recently purchased a Macbook 13" M1 and an iPad Air 4rd generation, each one under different accounts to be able to keep different stuff on our Clouds.

I was working on something today and I needed to use the IPad as a drawing tablet, therefore I thought of using the sidecar function, I was unable to make it work even if I declared her account as part of my family.

To be honest, I do not understand why Apple does not allow to use the sidecar function with different accounts, at least with the accounts defined as family. As users why might like to separate our accounts, as a family though, we would like to use our devices as if they were owned by the same person.

Is there any alternative to extend the Macbook screen in our IPad not using Sidecar?

Thank you,