The last thing I should be doing right now is writing a post like this on the forum, but I so badly want to put my own thoughts together on this that I am doing it anway (however, I would normally be doing a chore right now anyway, so I'll skip the chore and post instead!).
I don't personally understand my own reading ability at all. Even though there are these small flashes in my memory of needing to count some of the notes above and below the staff, and there are times that I think I forgot how to read music, in actuality that's not entirely true and I don't even understand why I would feel that way. And then there is this weird memory I have of learning to read Fur Elise as a little child, but I don't understand that memory either.
What I can tell you though is that I've spent a lot of time thinking about and experimenting with all things piano that I feel I can get my "hands" on. I am not an astounding sightreader at this point in my life (though there was a point before I became aware that it was a certain ability that I used to be quite good at it). Though in some way I've always known what I am about to say, it wasn't until fairly recently that I realized quite clearly that it's important to realize that our life at the piano involves different languages, so to speak. Eventually we want to see it's all actually one language and principle, for exmaple music involves both rhythm and tones, but these can and probably in many cases must be broken down and dealt with separately.
So, the language of knowing the topography of the piano is in some ways its own thing, though you could say it's tied to others. But, it's worth it to spend time (and it might take awhile) playing certain patterns while closing your eyes, and concentrating just on that, verses trying to get better at reading notes while at the same time getting better at learning the topography of the piano without looking -- even though they are definitely related when it comes to reading and sight-reading.
One of the first steps when dealing with something that seems complex is to realize that what appears to be the complexity of the situation is more like viewing a canvas of elements that can be isolated and managed in some ways completely on their own. So, yes, practice reading notes on the staff and finding them on the piano. Practice mentally understanding how that works. Most of my students don't grasp it more fully simply because they have no interest in putting in the (relatively small) amount of time it requires to get over that hurdle of needing to count through the lines and spaces. Your goal should be to outgrow the need for any mere method of doing that, and to reach a place of just knowing at sight which notes are being represented on the lines and spaces of the staff (so, without needing to count). But, you may have to start by counting! Just do it enough to where the counting decreases and you start to remember where each note is on its own. Okay?
While I don't want to limit you, don't expect yourself to be capable of doing everything at once -- as in, you are not failing at life just because you can't (okay, I think I'm probably telling myself that at the time ... haha ... though if you need it, take it in

). The motions at the piano are worth studying in and of themselves, and yes, you can learn quite a bit by watching others, but you can learn even more if you know what you are specifically looking for. I spent a decent amount of time (a couple of years?) turning pages for international performers and local pianists, and in some ways I learned quite a bit about piano technique from that, though I learned even more specifics by studying certain things like forearm rotations and other specifics.
You can also study intervals and scales and just listening, and it's necessary.
Eventually though, it all combines into something different than just these isolated quantities. It's not even a compilation of these quantities, but rather something of personal meaning to you, which can't accurately be quantified, I think. For example, when I think of my name (not m1469), which I've had for my whole life and learned to read and write it ... even when I just think of it very clearly, I can hear in my mind's ear certain elements of it very clearly, I can see it written (and me writing it) on a piece of paper, I can feel what's it like to write it with a pencil, I can feel what it's like to say it ... all of this just by thinking about it. However, the name itself while names may only mean so much, comes to mean something personal beyond those elements that I described.
Well, gotta go!