Unfortunately I can't demonstrate it to you with screenshots, because at the moment it's not possible to create such a search.
But it may help you to understand how repeatable field groups are implemented.
Again using the example of a custom post type "Company" with a repeatable field group "Offices".
When you add normal custom fields to a post type they belong to that post type (the posts are saved in wp_posts and the corresponding custom fields are stored in wp_postmeta together with the ID of the post they belong to).
When you create a repeatable field group behind the scenes Types creates a hidden custom post type for that repeatable field group, e.g. a post type "Offices".
When you edit a Company post and add a group of fields, a new Office post is created, and the group of fields belong to that Office post (not to the Company post). Add more Office groups, and each set of fields belongs to the corresponding Office post.
Types knows that these Office posts relate to the Company post being edited because it creates a relationship, with Company as the parent and Offices as child posts.
So, returning to creating a custom search, the underlying WordPress code for querying posts is the WP_Query class, and with that you can only filter posts by properties of the posts themselves. So if you have fields (not part of a repeatable field group) that belong to Companies, then you could search Companies by those fields. But the repeatable field group fields don't belong to Companies—they belong to the hidden Office posts—and so you cannot filter Companies by the repeatable field group fields.
You can create a View to query Office posts (the container post type for the repeatable field group) and filter by its fields.
That could return Office posts belonging to any Company, which may not be what you want, but you can also add a relationship filter to the search, to specify which Company the Office posts (the groups of repeatable fields) should belong to.
In the output section of the View you can output fields not just from the groups of repeatable fields, but also from the parent, i.e. the original post to which the groups of repeatable fields belong.
It would be easier to show you with an example, but because of the current issue it's not working, so let me tell you when the update is available, and then I can give you a demonstration if needed.