Isn’t there also a prohibition of something newly created here?

Why would that be something newly created?

A new entity is created—a coffee drink—that did not exist at all before the Sabbath.
After all, before activation I had two separate components: lukewarm water and dry ground coffee; once the percolator turns on, you get a completely different beverage, both in taste and in definition (like “food that turned into a drink”). So I wondered whether one should be concerned here about something newly created / muktzeh because a new drink comes into being on the Sabbath, beyond the discussion of cooking.

More generally, you could ask this about any machine that cooks on the Sabbath. Suppose there were a machine that makes a fresh omelet on the Sabbath from eggs that were placed in it before the Sabbath—would there be some prohibition involved? Maybe something newly created?

I don’t think there is really anything new here.

What about an omelet cooked by a machine on the Sabbath? There too there is nothing new?

Good question. Maybe there is.

This is basically a steam device for brewing coffee. The coffee drips slowly into a pot, which sits on a hot surface like a hotplate. There, I presumably need to act as one would with a hotplate if I pour from it. I can return it only if I did not set it down. Or if I did set it down, but intended to return it? [I intentionally presented at the beginning of the thread the most problematic possibility out of the three I had thought of.]

And this is apparently coffee that has only been roasted—coarsely ground black coffee suited to the various machines.
By cooked coffee, I assume you mean the various kinds of instant coffee.

And what if I also follow Maimonides’ view that there is no cooking after cooking—that is of course what I mean.
Because as far as I’m concerned, just as there is no cooking after baking, so too there is none after roasting. Maybe that is relevant only to making black coffee directly from the urn in a first vessel.