“Truth” is a word we apply to statements. We take statements to be either true, false or indeterminate. We don’t say “That tree is true”, we say “That is a tree”, and then seek to ascertain if that statement is true, or not. We may say “That tree is real”, but we still must verify that claim, and it is the claim we verify, and not the tree itself. In this way, there is no “unattached” truth - truth is always attached to a statement.
The means of verification vary - direct observation being considered the most reliable. We can be fooled by our senses, but we may still ask if an hallucination is really an hallucination, and then ask if the answer to that question is true. In other words, we can have a real hallucination, what is in fact an hallucination, but it is the statements we make about that event that we apply the notion of truth to.
And we may accept testimony in lieu of direct observation, but we then trust that someone has made an observation. This is our common notion of verification - the process of determining truth. And there are some statements that nearly everyone accepts as true - that the Earth is a spheroid, for instance, despite that few people have directly observed this. And when enough people have accepted an idea, for a long enough period of time, we call it a fact. And a fact is some datum that it would be unreasonable to disbelieve.
So we arrive at an objective fact, something that is objectively true about the world. But it’s clear that we have not done anything of the kind - we have arrived at a collective verification. A large and longlasting number of individual verifications, subjective verifications if you will, that we are able to, through language, communicate to each other. The idea of a “subjective” verification suggests some alternative, even an opposite by some renderings - objectivity. But objectivity is not a necessary corollary of subjectivity. For much that is arrived at by an individual is never shared - never accepted by anyone, and simply not a part of the Universe outside the brain of that individual - not an accepted fact.
“Subjective truth” means “individually verified”, if it means anything. “Objective truth” means nothing at all. It’s not that it doesn’t exist - it’s that the phrase is nonsense to begin with. Everything that is verified is verified by someone, or a collective “someone”, and that which is true is that which is verified. That verification itself is problematic - for verification can be accepted at one time, by some people, and then later rejected - but if any truth exists at all, it resides in that verification - an activity of people. Objective truth is collective truth.