Ehh, its a bit more than that.

Its a particle in that we know they are quantized into single photons. As in, it is impossible to observe half of a photon, or any non-integer number of photons, and one photon can only be observed in one place. This makes it like a particle.

But its a wave in the way it behaves - it can interfere (not just with other photons, with itself), and its movement can only be described through wave functions that can even take seperate paths at the same time, according to how waves propogate.

And, there are ways in which they act like particles no matter how they are observed, and same for wavelike behavior

Worth noting: "observation" is just physical measurement. You have to keep in mind that observing something fundamentally requires interacting with it - in order to look at an apple, photons must bounce off of it, which is a physical interaction. On the quantum scale, these interactions cannot be ignored.

Also also: this isn't just photons, everything is like this. It may not align with how we observe things on a macroscopic scale, but this is fundamentally how the universe works.

You're right that light is not "a wave and a particle depending on whether you observe it". Instead, light is a quantized field. It is a field because it exists at every point and allows for wave-like behavior such as superposition and interference (both things seen in all fields, like waves in water or radio, etc.). But it is quantized because when the field interacts it does so via photons which can only exist in integer quantities. This quantization of interaction of the underlying continuous field gives us all the "weirdness" we see. Okay, not quite all of it, there are still even weirder parts of quantum mechanics, but it does explain the double slit experiment.

The problem is the word "observation." Most people interpret that to mean a person look at it. This isn't the case. What it means is if it interacted with something where knowledge of its position is required. If this happens then the waveform collapses and a specific position is set. Before then it doesn't have a fixed position and the position is described as a probability distribution.

I have a hard time wrapping my head around the concept of how an observer is inextricably intertwined with the object/particle being observed, as part of the framework for the equations to flow, so to speak.

Then there's the fact that Newton's equations assume an infinite speed of light, until physicists of the 19th century that pinned it down, then Einstein established it as a constant.
If you try and use lightspeed at the atomic level, many values blow up to infinity, the math stops working, the answers become like static noise.

Recently I found out that Schrödinger's famous equation is written in the framework of classical, newtonian physics, not in quantum terms. Like using a star screwdriver to flat screws, yet it seems to do an admirable job up to a point. And you have a whole lot of infinities to sweep under the rug and ignore, what is it called, Normalization or Renormalization? One of the two.

It's all incredibly complex and abstract, the numbers being measured by the guys in the lab were strange to the point of absurd, and if you think it's weird for us now, imagine how they saw it then.

So yeah, the math says that the observer is not passive from afar, the observer is part of the equation itself of what is trying to be measured.
Then the closer you look, the blurrier things get, like a greased pig you can't get it to hold still, not even for an instant, particularly at the smaller scales, things don't behave the way they do at our sensory and mental level. Things behaving as if going backwards through time. Particles and anti-particles popping in and out of existence. Particles transforming into other particles. Particles going through walls. The list goes on and on and on.

Weird stuff has to be conjured up to try and make any sense of this.
Light or electrons as amplitudes of probability waves. Axes of imaginary numbers, eigenvalues in Hilbert spaces, wave-particle duality, etc.

Reality is extraordinary, it will keep on always surpassing our expectations and imaginations. It just keeps on happening this way, wherever we poke at.