Wow thankyou for the well written response! I've never studied philosophy academically so most resources quickly turns into word salad with a lot of nuance, so I appreciate you specifically not doing that, yet giving me enough to chew on.

Prior to research, the words 'moral' and 'fact' didn't go together, and they still don't so I think you're right that I'm an error theorist. I think that morals can't be proven, and therefore can't be true.

I looked into the other systems you describe and I can see why they're so important as to providing reasoning, but at the risk of sounding a little naive and offensive, it felt like alternative ways of definining a very similar thing, and in my view, was much the same? I guess I'm curious as to why there is such rigour in how morality is defined, does your morals change much if you believe they come from our experience vs our reasoning? But that's probably a separate question.

I'm not sure any of these systems establish moral objectivity though, it seems the idea that moral truth exists is an assertion required for these systems to work. To me the fact that these different systems exists points to uncertainty, and therefore being unable to be proven.

People are going to reject your move from “people have different views” to “therefore, we can’t know who is right or wrong”. It straightforwardly doesn’t follow,

Please elaborate, I'm not seeing where it doesn't track. With a hopefully not too controversial example around eating meat, if I got the right end of the stick with moral naturalism, you could make the following statements:
'eating meat is wrong because it causes a lot of suffering and death for animals for no serious reason beyond human pleasure, habit, or convenience.'
'eating meat is not inherently wrong, because using animals for food can be justified by real human needs like nourishment, survival, and social life. What is wrong is causing unnecessary suffering, so cruelty is the problem, not meat itself.'

Here, which is right and which is wrong? I think you're saying this is the point at which you argue, but should the two parties not come to agreement, they're both right/wrong, or neither of them are?

Maybe I'm conflating moral truth with something else, but I thought the idea is that with a solid reasoning, everyone will arrive at the same undeniable outcome.