I think the combination of both tags works, for me. I was a bit confused by polyamory
alone, because I went in expecting - well, more than one point of contact between the four of them. But harem
by itself just reads like a genre convention, and not a description of an actual non-monogamous relationship. Having both of them is more descriptive, to me, but then...
I don't know, is it a necessary distinction? Is this what people want if they go searching for a harem manga? Do people need to know what the specific vectors are in this unambiguously polyamorous relationship are, before they even read it? Hmm. I could see an argument for harem
either way.
The manga was cute, anyway.
There are RL poly relationships where some participants are not dating each other. I should know, I've been in one.
The simplest version of this is a V shape, where two people are dating the same person, and are totally aware of and fine with each other. And very likely are on friendly terms. But it can get more complicated than that. Poly doesn't have to mean "everyone with everyone".
To me, harem has a lot more to do with presentation, and usually in manga it's several people competing to be in a monogamous relationship with the central person. They're competing, not collaborating.