"Present perfect" is a tense (or, if we are really pedantic, it's a tense and an aspect), because it's about time of action (the process described was happening in the past, but now it's finished, and it has some result). In a sense, this is not even about the language, it's an aspect of reality, except we don't say that all languages have present perfect tense, because in many languages there is no grammatic form to express it. If English had a way to express hearsay grammatically, we could say it has renarrative/inferential mood. Furthermore, these are two kinda independent axis. If English had a grammatic variation for depending on if it's a hearsay only for the present perfect, we'd say it has renarrative mood in present perfect tense, but doesn't have in any other tense (even though, obviously, in real English we can kinda express similar meaning by adding the word "allegedly" to any tense, but there's no grammatic variation, so we say english doesn't have such mood, but then, one can argue that the same can be said about the word "have", so the line is a bit blurry).
See https://en.wikipedia.org/wiki/Tense%E2%80%93aspect%E2%80%93m...
It’s obvious that tenses that serve other functions can also be called a tense, and yet keep their supplemental grammatical roles. Why is there a resistance to accept this in my case? :)
You can read Turkish or Bulgarian grammer books. They all are tenses. There is no such thing as mood.