From my studies, I remember that solar systems have some kind of identity card based on the % of atoms and isotopes (versions of an atom with more or less neutrons).

The bigger the atoms the more exceptionally energetic the process that created them needs to be: normal star, big star, supernova, neutron star merger… Also some specific isotopes can be created by some processes and not others. https://en.wikipedia.org/wiki/Nucleosynthesis

So one part of the universe where a solar system formed may not have seen the same atoms creation processes as another, so their detailed compositions are different.
Cosmo chemists analyze the compositions of meteorites that formed at different times to try to understand the history of our solar system. For exemple, they may find that this isotope could not have been produced by our sun’s birth, and it must have come from a supernova or very specific kind of star. https://www.quantamagazine.org/what-crystals-older-than-the-sun-reveal-about-the-start-of-the-solar-system-20260302/

They make our origin much cooler by looking at space pebbles.

This is a difficult thing to accurately assess. While we can use spectrometry to find chemical compositions of stars and nebulae and planet atmospheres/surfaces, we cant even be certain about the interior of planets and moons within our own solar system, much less the galaxy.

We can make educated guesses based on the mass/volume and the stability of elements but I don’t think it’s an exact science.

However, i would imagine the answer to your question is No, the galaxy is not homogeneous. My reasoning is that near the center of our galaxy, stars are much closer together. This not only makes stellar collisions more likely to occur, but also means there will be significantly more cosmic rays in that space than out here near the rim.

Both cosmic rays and stellar collisions are the (theoretical) primary sources of certain elements. Berylium and Boron are created by cosmic rays fission, and as such id expect their concentrations to be higher in denser star clusters. And I’d expect higher concentrations of heavier elements due to both increased collisions AND due to the decay chains of unstable isotopes created by cosmic ray fission.

Cosmic rays are responsible for producing common isotopes like Carbon-14 here on earth, and we live in a pretty empty part of space near a relatively inactive star. So I’d imagine the amount of radioactive isotopes of all kinds would generally be higher in more dense stellar regions too.

All that being said, the most common elements will probably be the same. Hydrogen and helium are the most common in the entire universe, and many light elements like Oxygen and Carbon and even Iron which can be produced by fusion will probably be higher in concentration than any heavier elements regardless of where you are in the universe.

Homogeneous is more about the pov of the experiment. If you zoom in far enough at sugar water it is not homogenous even if completely dissolved.

So it really depends on how far back you are zooming out to declare something homogenous.

Think of it like the surface of the Earth. The same building blocks are everywhere but their distribution evolved and changed drastically over time based on initially small variances in heat and density. The distribution is deterministic, but appears “random” to an observer that spawns 14 billion years into the chaos of the explosion.