The issue is that normal newtonian physics only works in an inertial reference frame. For normal everyday calculations, we can consider earth to be inertial frame of reference (it's actually not quite, but close enough), with a gravity force equal to mg acting on everything. With that in place, all the maths makes sense.

Newton v Relativity has nothing to do with the point I am making.

If the plane is only subject to gravity, it will go into freefall and the occupants will “float”. If the plane is only subject to UA, then the floor of the plane will be pinned against the occupants and they won’t float.

That’s true by Newtonian physics and also true according to relativity.

I entirely agree - I wasn't bringing relativity into this. I'm simply talking about an inertial reference frame - a frame of reference, or datum, that is not accelerating. So the surface of our earth is a good inertial reference point (ignoring very small error due to rotation and the centripetal acceleration towards the sun - barely measurable). You could also use a vehicle travelling at constant speed. To borrow from another thread, you and I could play table tennis on a moving bullet train, and the ball would fly just as it would if we were at rest in a station. To calculate the ball's motion we could choose the train as a reference point - a valid choice, as it is inertial (ie non accelerating),and a wise one, as it keeps things simple - we measure all velocities etc with respect to the train. We could if wished, choose the earth, but then things get complex, because all the velocities would have the motion of the train superimposed on them, meaning a negative velocity with respect to the train might still be positive with respect to the earth.

But it all breaks down if the train accelerates. If you hit the ball to me and the train brakes suddenly, then the motion of the ball with respect to the train will not be what we would expect at all - we would have to choose the earth as a datum, or perhaps compensate for the acceleration in our calculations - engineers sometimes use d'Alembert forces to do this. You sometimes see it being done with circular motion - they add a 'centrifugal' d'Alembert force, even though no such thing exists, to change an accelerating reference frame into an inertial one.

If "When the acceleration of the falling object is equal to the acceleration of the Earth, the object has reached terminal velocity relative to the Earth".

doesn't mean that a "falling object" is accelerated by UA, what does it mean?

Again, the FEers are sort of, oddly correct here. The whole thing is nonsense, clearly, but as a thought exercise it does work.

Remember, the earth in UA/FE is not an inertial reference frame - you can't do newtonian maths with respect to the surface and expect things to work. So we have to imagine ourselves outside the earth, stationary, watching it accelerate past our fixed datum point. The earth is accelerating 'up' at 1g. The earth's atmosphere will eventually achieve a steady state whereby it ends up with a pressure/density gradient just like our atmosphere does on our beautiful, globe-shaped earth. Once stabilised in that state, it too will accelerate at 1g - every small 'parcel' of air will experience a net 'mg' force pushing it up. So we have a planet and an atmosphere accelerating upwards at 1g. If you then drop a ball from a hot air balloon or similar, the ball will initially be stationary with respect to the balloon, so it will have whatever velocity with respect to us observing that the earth/atmosphere/balloon did at the point of release. But it will retain that velocity, while the atmosphere and balloon etc keep accelerating, and so will appear to 'fall' from our perspective. As it falls it will start to experience a force, increasing with the square of the velocity difference, as the air rushes past it. At some point the drag force will reach mg, at which point the ball's upward acceleration will equal that of earth/atmosphere/balloon. However, it will retain a constant velocity difference. With respect to the earth's surface it is falling at terminal velocity. With respect to us, it is accelerating upwards at the same rate as the earth/atmosphere/balloon, but is at a slightly lower velocity. So the earth might be going at 1000m/s, and our ball might be going at 970m/s, with each adding 9.8m/s to their speed every second - the ball has a terminal velocity of 30m/s.

Note: none of the above obviates the numerous issues with the UA model, or indeed the many obvious flaws in the FE model generally.