Group tiled windows in overview for display and movement

Currently, windows in a tile group are displayed just like any other (separately) in the overview.
It would be nice if one could see which windows are in a tile group together, and how they are tiled, at a glance.

Basically I'd like TA to group tiled windows together in the overview, so that they show up as one "block", just the way they're tiled relative to each other.

Ideally, I'd also like to be able to move entire tile groups in one go, i.e. when I select a tile group in overview, I'd like the whole block to be selected, and when I drag it, say, to the neighbouring workspace, I'd like them to move together, as a block.

See the (no longer updated) ShellTile extension for an example of the desired behaviour.

Start by reviewing how the extension integrates with GNOME Shell's overview and how it represents tile groups. Compare the desired behavior with the linked ShellTile extension. Done means tiled windows appear as one block with their relative layout and can be selected and moved together between workspaces.