cb_right still exists. This feature provides a tab position map so you'll know exactly where things are. Can you clarify what's so confusing about this new feature? You're basically just selecting a profile layout from a dropdown. You do not need to move your tabs. There's also the Custom layout that lets you create your own using HTML and substitutions.

Below is the Canvas (Other) layout, which is the layout used for profiles in previous releases of CB. I've highlighted where cb_right is.

 

One question: I see that there are 4 layouts available. Is it possible to add a new one?

Yes, use the Custom layout and you can provide your own HTML for it to display however you like.

For example, I'd like to have two layouts for two different registration modules on two different pages. Can I do this using the profile layouts?

The Custom layout supports substitutions and Joomla content plugins so I suppose you could display 2 different modules depending on what URL you're on by IF substitution conditioning against the itemid. Example as follows.

[cb:if menu_id="12"]The current menu item is Itemid 12[/cb:if]
[cb:if menu_id="1"]The current menu item is Itemid 1[/cb:if]

The menu_id would be the Joomla menu id. This lets you display content based off the viewed Joomla menu. As for displaying the modules use normal Joomla content plugin shortcodes for that.

Have added a feature ticket to review adding placeholder substitutions if a tab position has no content.

forge.joomlapolis.com/issues/9233