Hello. We have a house that was tarted up in the 1980s with lots of artex on the ceilings. I had asbestos tests done on some samples after moving in.
I found that the really spiky stuff in some rooms did have asbestos, the stuff with more rounded spikes in a couple of rooms did not. This tallies with what a retired builder told me, that the artexer blokes were all cursing when the asbestos was taken out, as it wouldn't stand up in peaks as well as it used to. Basically the asbestos fibres acted as reinforcement to hold the shape. The same blokes are probably cursing the older stuff now, if they were regularly whisking it up as powder and breathing it in.
I'm not sure from your photo, but my guess is that this does have asbestos in. The later stuff without it was more like thick paint than spiky.
My opinion is that it's best left where it is. Just plaster over it. It's not crumbling so it's not getting airborne so it won't do any harm to anyone. If taking samples then carefully snap chunks off, wearing a mask. Don't scrape and crumble it.
The really dangerous asbestos is in crumbly sheets or fluffy insulation. Artex is probably near the bottom of the risk scale.
We also have lino tiles under the carpet. These also contain asbestos fibres, again their purpose was to reinforce the tiles for strength. Also these have little real risk as they're not flaking and are not getting airborne.