Are there some pointers you could give me to understand FF7 a bit better?

Play the original instead.

No satire here; I genuinely think it's a great example of a remake done well.

There are some major breaks from the original plot, which in itself would be neat, but they introduce an entire plot element that interacts with this derivation. The spirits I was talking about, "Whispers" (had to look up the official name, tbh), appear whenever the story attempts to break from the original story from the original release. In universe, this is explained as pre-determination, or destiny. Thanks to our meta knowledge, we know in reality that these spirits are attempting to maintain the timeline from the original release.

As an early example, after the events at the first Mako reactor, Cloud decides to collect his pay and go his own way, which is not the original intended path of the game. To correct this, a group of Whispers attack the party, and ultimately injure Jessie, preventing her from going on the mission. Needing another body, Barrett is forced to rehire Cloud for Avalanche's mission to the next reactor. Without spoiling specific details, the whispers slowly become a form of antagonist as the characters try harder to get away from the original plot of FFVII.

This is interesting in a few ways. First, we've introduced a new major conflict in the form of the characters fighting against a physical embodiment of destiny. They do not want the outcome of their struggles to be predetermined, particularly as that predetermination involved the death and suffering of some specific characters. This is, in my opinion, an interesting new plot element beyond being "the same game again."

Second, stepping back, and examining this with a wider lens, we can look at the Whispers for what they are to us, the players, rather than what they are to the characters. We know they are not maintaining "destiny," but instead trying to reestablish the original story we loved. As a result, I see the Whispers as the collective voice of the "change nothing" remake ideology. When a community asks for new content of IPs they love, there will always be diehard essentialists who want their loved stories to remain untouched; the Whispers, then, are these people.

So if the Whispers are a physical representation of the "change nothing" remake ideology, then what is there to make of the fact that they're largely an antagonist? This seems to me that the writers were critical of this culture, so much so that they ask you to fight it to earn the different take on the story. Of course, it's far from the only derivation from the original game, but that's exactly my point: FFVII remake was so far divorced from the conceptual, soulless "let's pump out the same game again" remake that they literally wrote that culture into a new antagonist.