I see the AI gathering anomalies, but nowhere near as aggressively as I do. I believe they have a paradigm of getting unprotected anomalies first before surveying protected ones. They do claim relics, but the action is very hit or miss. Relics out in the void are seldom claimed. Often, there are relics in an AI territory that I find unclaimed after crossing the whole galaxy. Occasionally, they are within 10-15 tiles of a planet. So, I claim them and then they get mad at me. I tell them I just can't resist temptation, but I don't think it is convincing them of anything. I have relics at occasional and still, I get to claim a great deal of relics because they are so ignored.
They are eager to claim clusters of multiple resources. I approve of that to an extent, but I think they overdo it. I have a bunch of Durantium mines in this game because I am going to try doing a bunch of missile augments. I am not sure I really need augments in this game. It is exceptionally peaceful. But just in case they surprise me, I will be ready. That's as close to needing a ton of resources as I have gotten. So, two or three clusters of resources seems to be enough for my needs so far. Also, I have learned to leverage claiming a relic and using range extensions to dual purpose those starbases. Either they act as Mining Rings for nearby resources, or better yet, as an Econ Ring for a nearby planet. That is a trick the AI should learn.
I think the AI resource/relic claiming is still improving. It needs a little more balance in priorities and awareness of range extensions. And it can't leave relics unclaimed in its own territory while still hunting down all those resources!!! The administrator hard caps and such are still in flux, but planning ahead for them needs to be learned by the AI as well as we humans. We'll see what happens, but I do expect that we'll see more progress in this area. When that progress happens is anyone's guess.