Starlink receivers will use solid-state phased array beamforming antennae, so nothing has to physically "swing" to a new satellite. With a reasonably accurate accelerometer and inertial sensor, it's easy to compensate for aircraft movement.

I thought even the current GEO orbit antenna were phased array. If not, there might also be the point that the aerodynamics for a phased array shell may be less expensive on fuel burden (less air resistance, less turbulence) and lighter, so cheaper overall. (at a refit cost)

The Connexion antenna was all phased array with no tilt/yaw, but it was huge. The ones on aircraft now do track the satellite, tilt, etc.

Most of the ones I've seen still have moving parts. They're clever mechanisms and are not as deep as a swinging dish, but they're still motorized.

Ahh, that's helpful, but the spot size is likely pretty small, so there is probably some work on how to make the transition from spot to spot seamless.

Installing two antennas per aircraft could make the transitions pretty seamless, at the cost of a little extra weight and drag.

That's how it will have to be done in any case. The only question is whether they'll split the phased array transducers in one large array to look at two satellites at once, or have two separate smaller arrays. Both approaches can be made to work, and the first is probably better aerodynamically.

I don't think you'd even need that, the antenna can "simply" seek the strongest signal direction.

It's not that hard with a phased array. Not trivial of course, and there are lots of subtleties (like handoff) but it's known engineering.