What problem does this address?

Pulling in some feedback from the third call for testing as part of the FSE outreach program from @paaljoachim :

I expect the placeholder to show small thumbnails of existing template parts. Today there is a button that says Choose existing. Choose existing could be a title and thumbnails could be seen below. So one sees the title and then clicks a thumbnail to add the specific template part to the layout. I clicked the Choose existing and it showed up kinda weird right below the button somewhat similar to seeing patterns in the block inserter panel. I do also expect that when hovering over a thumbnail to see a bigger preview to the left as if I was previewing a pattern or block.

Here's a screenshot of the current experience:

Currently, the template parts run together in a way that's hard to distinguish them and they are quite small to view making it hard to see what you might actually be selecting.

What is your proposed solution?

Ideally, for the "New template part" option, patterns or some sort of placeholder option can be better integrated to help users get started. Currently, one just sees this:

For the "Choose Existing" option, an improved preview can be offered similar to what's done when browsing through templates in the navigation sidebar (aka just have the names listed with a pop out of the preview to the right):