It's now implemented, mostly!
It shows all the planets in the system that your colony ship(s) are adjacent to. It shows the planet's number underneath the planet - If it's white, it's colonizable by the selected ship. If it's grey, it's uncolonizable. If it have color, it's owned by an empire.
It can have multiple ships listed if you have more than one colony ship in the same system. So if you have a ship that can settle radiated planet, it would show radiated planets as colonizable if you have that ship selected.
If you don't want to colonize anything, just click on "done", the left most button. If you do want to, click on the right button to confirm colonization.
Let me know what you think of the UI layout!