So the question is: is there an umbrella term for this kind of work?
It feels to me that there should be, beyond terms like documentary, landscape, portraiture, fine art, etc. which are essentially categories by subject or style and make no distinction between a phone snap and something worthy of say a major gallery exhibition.
In my head, I use the term expressive photography to cover photographs where there was a clear emotional or intellectual intent on the part of the photographer to communicate/express something about the subject (and the photographer), which is deeper than this is what " a duck", "a tree", " a pizza", " little Johnny at five", or the beach at Newquay" looks like.
These photographs of duck and pizzas still "say something" to those who took them as mnemonics, but unlikely to carry the same meaning to others as good photographs taken by good photographers with a conscious intent to capture images that reflect how they see and feel about the world they live in. There is obviously lots of diffused categories lying between mnemonic and expressive, but I think these are the two end points.
BUT, in my head when I think of "Photographer" I am normally thinking about "Expressive Photographers". Just as when I think of "Painter" I am thinking of some one with brushes and easel creating art, and not the person who painted my front door, or the person from the council that paints crosses on dangerous trees that need to be felled.
So rather than try and define the type of Photography you mentioned, I generally do the opposite and try to qualify the types of photography that don't fall into my loosely defined genre independent expressive photography categorisation. e.g. wildlife photography, sports photography, wedding photography, mnemonic photography, landscape photography etc.
That isn't to say these "other" types of photography cannot also be expressive (or dramatic or relaxing, or creative), and they are often the foundation of expressive photography, but when compared to expressive photography, in general they seem far more about competently "recording" the subject, and not so much about a photographers emotional and intellectual interaction with the subject.