If you create a repeatable field group with Types and you add some data to a post, then when you want to display the fields from the repeating groups for the post you would need to create a View where you select the repeating field group as the Content Selection.
You would then need to add a Query Filter to specify which post the fields come from. At the moment that means adding a "post relationship" filter and then choosing the repeating field group, but this will be made a little clearer in the stable release.
You can then output fields in the Loop Output editor much like you would any other View.
If you want to display this View in a Layout you can.
If you want to design the View output with a supported page builder you should be able to.
If I understand you correctly, what you are suggesting—that the output of a View can be designed using Layouts—isn't possible anyway, irrespective of whether the View is used to output repeating field groups.
So, no, it is not possible to design the output of repeating field groups using Layouts.
As part of the work preparing for the shift to Gutenberg we will be re-thinking the future of Layouts, and designing Views Content Templates with Layouts is an option that will be considered.
But that screenshot looks exactly the same as for a normal View. There are normally no layout options available there, so I'm still not sure what options you expect or want to see.
If you scroll down a little further to where the Content Template is you would see a button to edit with a page builder if you have a supported page builder installed.
Or you could go to Toolset > Content Templates and edit the same template from there, when, if your theme supported integrated theme options, you could set the theme options (e.g. no sidebar).
If you mean something different by layout options, what do you mean?
The option to have a layout edit at the image shown above, so that we can design the repeatable fields directly via layout. But currently, we have to design repeatable fields by the content template and cannot do by layout.
Then, as I mentioned above, we are considering being able to design Content Templates with Layouts, and I think if implemented correctly that would mean being able to do what you want.
This is a discussion we are going to have in a few weeks when Types 3.0 is released, and I'll be sure to raise your specific use-case then.
Currently, we aren't able to find a use for layout as it is same as normal page builder.
However, we have to use a content template every time and it would have been so much great (easy) to have layout and content template integrated somehow. OR we can get an option to use the layout where content templates are being used.
And, all our requirements are mostly covered with types and views.