Separator Block: Color is not reflected correctly

[t-hamano]

Description

The color of the separator blocks is not reflected correctly in both the Classic and Block themes.

I think that this problem might be caused by the fact that the color setting has been moved to block support and the .has-background-xxx class is no longer assigned in #38428.

Step-by-step reproduction instructions

1. Activate Twenty Twenty Two (Block theme).
2. Confirm that solid colors are reflected correctly, but gradient colors are not.
3. Activate Twenty Twenty Two (Classic theme).
4. Confirm that both solid and gradient colors are not reflected.

Screenshots, screen recording, code snippet

Block Theme (Twenty Twenty Theme)

tt2.mp4

Classic Theme (Twenty Twenty One)

tt1.mp4

Environment info

WordPress Version: 6.0-RC3
Gutenberg Version: 13.2.2
Theme: Twenty Twenty Two / Twenty Twenty One

Please confirm that you have searched existing issues in the repo.

Yes

Please confirm that you have tested with all plugins deactivated except Gutenberg.

Yes