I thought Overlord Edition was the most complete way to buy the game but after typing Tyranny into the search there are still several things not marked as owned.

Commander Edition
Overlord Edition Upgrade
Bastard's Wound
Portrait Pack
Tales From The Tiers

Shouldn't I already have these?
How much more stuff do I need in order to have everything?

Nope, because Paradox. Commander Edition includes a lot of "extra" stuff, but doesn't include any DLCs AFAIK.

So if you want Tales from the Tiers DLC, or Bastard's Wound DLC, or the portrait pack DLC, then you'll have to grab each of those separately.

Sure, they should have been included with something priced at the level of Overlord Edition, and the portrait pack is a joke that they shouldn't even be charging for, but this is what happens when the publisher is Paradox.

What about "Commander Edition" and "Overlord Edition Upgrade"?

I think they just give you extras of some sort, like concept art or something. They should list what they include on their store pages.

I'm pretty sure none of them include any of the DLCs - if they do, it's usually explicitly mentioned in the store page(s) (though sometimes this isn't totally clear).

I mean about them being not owned. As far as I can tell I have the included content but the store is still advertising it as something extra.

No idea - you'd have to contact GOG Support to find out what the deal is with that.