You can get cheap consumer cameras now with pretty absurd zooms. The $600 Nikon P900 [1] has an 83x optical zoom lens, giving it the 35mm-equivalent focal length of 24-2000mm: https://www.youtube.com/watch?v=4SC_2yD6wKk.
It's shockingly good for what it is, which is why the camera was sold out for six months and still commands pretty much its original retail price nearly a year after release.
Its big weakness is autofocus speed (making it useless for birders, etc.)
In my experience the autofocus speed in daylight is fine and it's especially good at focusing on what you want it to focus on, so it's great for birders. The problem is noise-reduction i.e. image quality. Do a bit of pixel peeping and it begins to look like a watercolor painting.
I was lucky enough to get one the day it was released early last year. Fun toy, and great for travel/sightseeing where you often can't use your feet as a zoom, but not even close to 1" type sensor quality let alone SLR.
Saving my pennies for a Sony RX10 III 24-600mm equiv superzoom, thought it's roughly 3 times the price of the P900. Good review here: https://youtu.be/Ad1JDfmyNxI
Not even close to a DSLR. It uses a small compact-style sensor (6.17 x 4.55mm), which is about 14 times smaller than an APS-C sensor (e.g. Nikon D5500 at 23.5 mm x 15.6 mm).
Ok, the Falcon 9 1.2 [1] is 70m tall [2], and the rocket fills up about 80% of the vertical frame [3].
Using the "Image = FL * Obj / distance" equation, we get:
.8 * 24mm = x * 70m/4080m
Where x is the focal length of the lens assuming a full frame camera.
This comes out to a x = 1119mm equivalent focal length. If you have a crop sensor, this isn't too hard to obtain. I'd be amused if the video was taken with a Canon EF 1200mm lens or something, but the probability of that is 0.
It's pretty easy to mate an interchangeable lens camera (DSLR, Micro Four Thirds, etc) with a small telescope. There are standard adapters for it. That basically gives you the telephoto lens to rule all telephoto lenses.
The shot is totally within the capabilities of a 200 mm Schmidt–Cassegrain in good seeing, which is not very bulky and could sit comfortably on a medium-to-large size tripod.
The theoretical linear resolving power of that aperture at 5 km is 12 mm. But in practice it will be several times worse.
This is all napkin-based math, I've no clue what optics were used for the shot. Might have been a compact 150 mm apochromat refractor - still capable of enough theoretical resolution, and possibly a more popular option (though more expensive) in practice.
