According to PIV, both "sida" and "sidanta" have the same meaning, and both are derived from "sidi".
- Mi estas sida. = Mi estas sidanta. = Mi sidas. = I am seated. (description of my position -- be in a position in which the upper body is upright and the legs are supported)
- Mi sidiĝas = Mi iĝas sida = I sit. (action -- move oneself into such a position)
The source of these English definitions is Wiktionary.
This may be splitting hairs, but since "sida" is such a rare word, I thought I'd look it up in PIV as you suggested. PIV doesn't seem to be saying that they're the same. Rather, it uses one as part of the definition of the other. I'm becoming convinced that it doesn't pay to think too hard about "sidigxi" because there are expert speakers who see this as an Esperanto idiom.
My take is that "sida" is an adjective related to the act of sitting. So a "sida pozicio" is the kind of position you'd be in if you were sitting. It's very rarely used, and the examples that I see of it in use never refer to the person sitting, but rather to a position, pose, or even a sedentary life.
So, based on the screen shot above, it seems that the definition was modified by the editors of the newer edition. One thing that should be clear even to the layman is that you can't use a word in its own definition so defining sida as being in a sida pozicio is just a bad practice. I am confident that you will find that this was a mistake or bad decision by the editors. Actual examples of "sida" in use in PIV and in model texts show that "sida" and "sidanta" do not mean the same thing.
I'm asserting that you can't use "sida" to describe a person. As I mentioned (indirectly) elsewhere in this thread that in the tekstaro, you'll only find examples of it being used to describe a position, pose, or life.
There are other words we could form the same way -- "kura" springs to mind. It does not mean "kuranta" but rather "pertaining to running".
I can find only three sentences in Tekstaro (two describing "pozo" and one describing "vivo"), so I can't judge. But what you say seems to be very logical.
I think the problem is that PIV says that "sida" and "sidanta" are the same. I would suggest that you contact them. Registration is not required.
Thanks for the helpful discussion! :)
The debate here is much bigger than a simple e-mail from me to the online mailbox of NPIV. Certainly bigger names than Salivanto have given feedback here. In the meanwhile, I read through an article which supported my position here - in contrast to what the authors of PAG recommend. PAG and PMEG differ on many points, but haven't found a reference there. (It references "sida pozo" in the explanation of "je". I also checked Krause, and it doesn't make a strong distinction between sida and sidanta, perhaps because they both can be expressed by different shades of the same German word.