Cat wakes us up meowing every night at 3am — we have tried the obvious things and none of them worked. What are we missing?

The ignoring advice is not wrong, but it is stated in a way that hides its precondition, and yours is the case where the precondition fails.

Ignoring works when the meowing is learned attention-seeking — the cat does a thing, a human appears, so the cat does the thing. Take away the reward and the behaviour eventually goes. The ten days of escalation you saw is the textbook pattern and you handled it correctly.

What it cannot fix is meowing that has a cause other than you. If the cat is hungry, cold, bored, in discomfort, or responding to something outside, then your attention was never the reward, so removing it changes nothing. She went quiet for three days because she was tired, then resumed because the actual cause was still there.

So the useful question is not "how do I extinguish this" but "what is she telling me". Your three quiet days are evidence: pure attention-seeking does not come back stronger after a successful extinction burst.

The 4am feeder may be actively causing your 3am problem.

Cats are very good at anticipating a reliable event and they wake up before it, not at it. A feeder that fires at 4am every night teaches her that something happens around then, and the anticipation window creeps earlier over weeks. This is a well-known way to accidentally build an alarm clock.

Two things that work better than a fixed time:

• Randomise it. Some feeders can fire at variable times; if yours cannot, several small portions at unpredictable hours beats one predictable one.
• Move the reward off the clock entirely. A puzzle feeder or food scattered in hiding places before bed gives her something to do at 3am that does not depend on anything happening at a particular moment.

Worth trying the feeder switched off for a fortnight as a test. If 3am becomes 4:30am or moves around, you have your answer.

"Played with her hard before bed" is the one I would examine, because there is a common way to do it that backfires.

A long chase session with no ending leaves a cat wound up rather than settled. The sequence that works is the hunting one: stalk and chase, a catch she is allowed to win, then food, then grooming, then sleep. Cutting the toy off mid-chase and putting it away is like stopping a film ten minutes from the end.

So: fifteen minutes of wand toy, let her actually catch and hold it at the end, then her main meal of the day. Not a snack — the meal. The sleep after eating is not willpower, it is physiology, and it is the strongest lever most people are not pulling.