Problem/Motivation
For a frontend theme wishing to provide its own layout builder element widgets, toolbars, etc, the structure of the layout builder render element can be very limiting, forcing some very hacky and fragile overrides.
There does not appear to be a specific theme hook, preprocess or template for themers to cleanly override the element output. You either get to muck around with the very generic and nested "container" and "link" theme hooks, or override and extend the render element class to implement a dedicated theme and template yourself.
Proposed resolution
Implement hook_theme()
for layout builder module, provide specific twig templates for the layout render element, the section configure links, and the section/block add links.