Plumbing – Is this a threaded tap? If so, what is the best way to unscrew it without damaging it

The next step secret to getting more of this faucet apart are the two slots cut across the cupped part. See the arrows in the following picture.

It looks to me as that the cupped part is threaded down inside the larger diameter part that sticks up from the hole in the sink. There is probably a special tool used to engage these slots to thread the part out. It may be possible to lay a piece of metal bar stock across these slots as a tool. If you do that make sure that it has nice square corners.

See if a careful knife or razor blade might pop it off, the spring clamps could be pretty strong. If that fails to widen the gap, then it's a screw-on cap. You'll need to treat it like a faucet aerator that you don't want to scratch, by wrapping the cap with cloth, leather, rubber, plastic or even liberal tape & take big (long) pliers to it. It should be normal threads, loosen to the right.

Otherwise, I might try the shoulder sleeve below the stem...that looks removable. Not that I've seen it before, but the cap could be screwed from the inside as that stem looks quite thick.