Well, it sounds like plans are changing, but I'll lay out what the previous plan was. If you're familiar with the galaxy map from Stellaris, this should be familiar to you. First, this is what it looks when you have a zoom level such that there won't be any overlapping. (Of course, note that it's highly unlikely all these icons would show up at the same time
From this level on the north quadrant of the planet you'll see icons indicating presence of king units (not as important now since they are no longer mobile Arks) as well as icons indicating the presence of mobile military (imagine pretty icons instead of little circles). Those icons are clickable to select that mobile military, allowing you to perform troop movements from the galaxy map in a gross way (click on a rebuilt fleet at home and right click on a planet near the front to move it up for example). Enemy mobile military is shown, but it would likely be more useful to see "freed" enemy mobile military so you can more easily track down threat. It also shows you the planet's aggregated strength value for your side and the any hostiles. This means at a glance you'll be able to look across the map and assess relative defensive strength levels, engagements, ally positions (for multiplayer), and be able to round up all your straggling ships. Since mobile kings were going away, that was likely to be replaced with engineer and scout icons on the left there.
In the west quadrant, you would find a variety of icons for why you would bother capturing this planet (or why this planet is valuable if it is already yours). Capturable structures, bounties of science, etc. These icons would also be clickable and would add the appropriate mission to your missions tab on your sidebar. Click again on the icon and the mission would be removed. If you already have the planet, then your structures would be there so you know you have to defend this one.
In the east quadrant, you would find a variety of icons for particularly nasty AI defenses. Anything that would make you change your attack approach or reconsider what the AI strength actually means would be there. Like the west quadrant, you could click on these to issue missions to your mission ledger.
In the west and east quadrants, the icons would likely be stacked three rows high and then start expanding outward, so they don't jut too far from the planet.
The south quadrant gives you the name of the planet and its Mk level (if AI controlled, owner's icon if player controlled, the planet itself wears the color of its controller is the current plan, but that's was subject to change). There are also two important icons. An ignore icon that de-emphasizes the planet and hides some things like the west and east quadrants, this would be great for a planet you've decided you aren't interested in taking. The foot icon is the pathing command. Click that to toggle on/off if your ships will path through that system without you explicitly telling them to. Useful for making sure your ships take the route through neutered planets instead of through the Mk4 planet that is technically a shorter (but deadlier) route.
The wormhole lines coming into and out of the planet would be color coded (not red and green as pictured here to deal with color blindness) to show if the route led to an enemy or friendly planet. There were some graphical plans to make sure those lines and the quadrants popped (such as background boxes or thicker borders for the wormhole lines.
Then, as you zoom out, this folds away to ensure that you don't have a jumble of overlaps. At minimal zoom you likely will just see the planet, the wormhole lines and maybe the mobile military icons (depending on what it would have looked like when we tested it with a stupidly high number of planets). (Oh, and don't think you'll have to be super-zoomed in to see all this information, just enough that it's clear what data goes where)
While you have this map open, you'll still have access to your sidebar, allowing you to click on a planet of yours and then being able to access the build menu (and all the other sidebar tabs) without having to switch to planet view
But! It looks like the concerns with zooming in and out from this thread have added to concerns over the difficulty programming it so Chris will likely be moving to a more static map like AIWC. I'm currently trying to figure out how much space we would even have to display info since the maximum number of planets cap has been taken off. It would help me if people here could tell me what aspects of the plan I've outlined they would most like to see preserved in a static-map version. I am personally not a fan of moving back to not having the ability to select/control ships and build queues from the galaxy map, or only having a tiny bit of information floating over each planet based on a couple of dropdown boxes (or having to mouse over each planet to find critical facts about it), so I will try to find a compromise between the AIWC vision and the Stellaris-like vision I've presented here.