Thermodynamically speaking, the energy in tides does come from Earth's rotation.

The moon raises a bulge in Earth's crust and ocean. Earth's rotation carries that bulge ahead of the Moon's position. The bulge pulls the Moon forward (raising it to a higher orbit), while the Moon pulls the bulge backward (slowing Earth's rotation.)

Once Earth's rotation slows enough, tidal lock is reached. Then the tidal bulge stays in a single place always pointed at the relatively non-moving overhead Moon, and there is no motion to extract energy from.

The short answer is that there would still be tides without rotation, but with a period based on the lunar cycle. We have daily tidal effects, the moon can't do that by itself.

Ah I see, that makes sense. Thanks.

The mental model I was presented with is that the ocean bulges toward (and, on the other side of the earth, away from) the moon, and the earth spins within the ocean. If you take a perspective that is fixed to a particular point on the earth, you'll see the tides constantly moving past, but that's an illusion just like the rising and setting of the sun. They're both really the rotation of the earth.

Also relevant is that the oceanic bulge is along the elliptic, but the earth's axis of rotation is tilted. So the effect can vary by latitude.