I have tried adding additional CSS classes to the container, conditional and single blocks, but they are not appearing on the selected blocks on the front-end theme. I have tested this in my custom theme and Twenty Twenty One.
When I save the post and continue working, I see the CSS classes are being removed from the container block and blocks nested under the conditional block.
See this screencast for an example: hidden link
This is very frustrating. So far I have had nothing but trouble using Toolset on my client's website. This is concerning for a commercial plugin that should not be afflicted by these issues.
Hitting return after entering the class name(s) did work, but this behaviour differs from the core block editor for adding classes. Also, why is there no hints that this is required for users.