Mount Sky-Watcher Star Adventurer
    Tripod Manfrotto MT055XPRO3

The tripod is a good, heavy, stable one. https://www.manfrotto.com/us-en/055-aluminum-3-section-tripo...

The head is https://www.skywatcherusa.com/collections/star-adventurer/pr... which is a bit more fancy than the old school equatorial mounts.... but

    Star Adventurer 2i multi-function equatorial tracking mount with built-in Wi-Fi control

It's still an equatorial mount.

https://astrobackyard.com/equatorial-telescope-mount/

https://en.wikipedia.org/wiki/Equatorial_mount

You adjust the base to the latitude that you are at so that the mount can rotate to match the Earth's rotation on one axis, and then the other axises can track ascension and declination - which remain constant in the sky.

This differs from the altazimuth mount ( https://en.wikipedia.org/wiki/Altazimuth_mount ) where a celestial object is that that location now, but moves.

Sirius is at 06h 45m 08s RA and -16° 42’ 57”... but as I type this, as seen from Greenwich, United Kingdom it would be at -27.4° altitude (below the horizon), 277.5° azimuth - and that coordinate system moves.

An equatorial mount keeps the camera pointing in a fixed celestial direction by rotating at the same rate as the Earth in the plane of the equator. It's essential for any long exposure of the sky where you don't want star trails, the unusual thing here is having the horizon in frame.

The camera was on an equatorial telescope mount.

"An equatorial mount is a mount for instruments that compensates for Earth's rotation by having one rotational axis, the polar axis, parallel to the Earth's axis of rotation."

You could also get the same effect with a regular tripod, time-lapse photography and a rotation effect. The sky would look normal though, not like in this. https://en.wikipedia.org/wiki/Time-lapse_photography

Sibling comments say/explain how it is done 'properly', but surely you could just 'lock to the ground' and then animate it flipping 'in post'? It's not like we need the fancy camera mounts to know how the rotation goes?

Instead of turning with the earth, it stays "in place". Meaning it turns to the opposite of the Earth's rotation.

It is easier to understand if you imagine that the observer is at the south pole looking up, instead of thinking of them on the equator going around. In reality, they are somewhere between the two extremes.