Classification of musical instruments into these sorts of categories gets tricky in some areas (especially with regard to percussion). Really, the percussion and keyboard categories (when people acknowledge them) kind of become weird catchall categories, especially percussion. Also, depending on our goal, it's ok to let one instrument belong to multiple categories.
*As an exercise:* do you classify based on the means of playing the instrument or by the actual source of the sound?
If it's by the means, then the *piano* is a keyboard instrument, but if by the source of the sound, it's percussion... or is it a string instrument (chordophone) being played by means of percussion which is being triggered by means of keyboard? Is percussion only ever a means of playing? If so, what are drums, membrane instruments? And are cymbals a different category?
And then what about a *harpsichord*? It's another strung-keyboard instrument, but its strings are plucked rather than hammered. How should it be classified?
And then there's *bass guitar*, clearly an electric chordophone unless it's being slapped in which case it's obviously percussion... but its sound is actually reproduced by a speaker cone at the end of an electrical path that varies in complexity... unless it's being recorded directly to tape/digital without a speaker being used at all. Does the classification of a bass guitar depend on listening format?
It's kind of like when people say, _"Actually, a tomato is a fruit,"_ or, _"There's no such thing as a fish."_ Botanically/taxonomically, sure, those people are absolutely correct, but then a ton of other things that we refer to as vegetables (most of them, off the top of my head) are also technically fruit. In fact, botanically speaking, there's no such thing as a vegetable (huh, kind of like fish... I guess we could consider them seafood).
*To sum things up*, I guess my point is that categorizations are somewhat flexible (in many cases even subjective). More importantly, they're only meaningful when they help us to solve a problem. By extension, they only apply to a particular context. A tomato is both a fruit and a vegetable; you just need to decide whether you're a botanist or a chef.
So we're back to the old question what is science and what is not; there is definitely a different perspective depending on whether you come from US or Europe; here in Europe, we are much more (i.e. too) liberal with the term "science"; so there is e.g. "Musikwissenschaft" or "Geisteswissenschaft", and in parallel an eternal discussion whether it's indeed "Wissenschaft" (science) or not (and whether it makes sense for a society to enable so much people to study it). I myself play piano for nearly fifty years (even as a professional musician for some years) and never met any professional subsuming it under percussion; rather, it is a category "sui generis".
I am also a long-term pianist. I have always heard it categorized as percussion.
That being said, percussion isn't necessarily the most useful category of a piano for purposes of physical modeling: after all, it's just a traveling wave generator along harmonic strings and an amplifier board. If anything it's more like a hammered dulcimer or hammering a guitar.
But of course it's just language, which is "the source of all misunderstandings", as they say. The physical modeling is a bit more complicated than you envisioned; e.g. https://www.modartt.com, which is a great simulation, even has different physical models for different piano brands, taking into account the specific differences in materials and construction methods.
