OP, I’m a beginner on pipes as well but have more experience on other instruments, learning music etc. While I grew up listening to Irish music I have not started playing it until later in life.
As you don’t mind buying books (it seems), the most systematic and useful book from a pedagogy perspective I found when learning to play Irish tunes was the Mary Bergin Whistle tutor. It’s not specifically pipes but it teaches a systematic style of playing by a master player and there seems to be a lot of useful overlap between the piping tutorials I’m going through. The first two books get up to playing reels in a rhythmic way. If you want a systematic overview or method (as opposed to a more academic/reference guide type of systematic) I would highly recommend it. I am constantly referring to it to see how the articulations differ in the piping versions of tunes, etc. It’s systematic without being stuffy. She will show you where the common places for cuts, rolls, articulations, etc. belong for the tune types, while also not burying the details in the specific tunes.
I have noticed (maybe you have too) that many of the (excellent) piping resources available teach on a tune-by-tune basis, which is a great way to learn and may not seem “systematic”. But after learning, for example, 12 jigs and the “technique” that comes with each one, you’ll start to see where the ornaments tends to go and how they serve the tunes and rhythm / tune types. Bergin does this as well but with an overview of why she is ornamenting in that particular way and why she makes exceptions.
As an aside, one risk I found in teaching a “theory” or “system” first approach when I was teaching guitar is that it becomes easy to be formulaic. For example, a kid wants to learn a 12-bar blues so you show them the structure, a “blues” scale and some “licks” instead of doing the listening and learning of specific players and songs. It can create a superficial or formulaic (and lifeless) style. No real blues musician learned this way (I’m willing to bet). Or if they did they needed some serious correction work later.
I find that some of my favourite tunes have a structure and tradition of interpretation that gives them a life of their own. They are not “just” a “standard” jig, etc. So if they were treated as such (“here’s where the cuts and rolls should go for a jig!”) they loose their identity. Sometimes (e.g. at sessions) things can get a bit standardized and the tunes loose a little life.