Hahaha, you've assumed my values incorrectly. Maybe our values could just align and that's what brings us together here on Nostr.
We should be clear to draw a distinction between values and value; similar word, but two different meanings. Values: beliefs that motivates people to act one way or another; value: the importance of a good or service. Values can influence the way we value goods and services. I've tried to structure the definitions that don't assume either is objective/subjective.
Without you providing an examples of an objective purpose, I'm not sure I can argue the case properly for whether objective purpose exists or not, and even if I could I'm not sure I would be willing to convince you. I'm pretty sure the answers lay somewhere in existentialism and contexualism, a topic I don't think subjective value theorem (SVT) touches on.
In the field of behavioural sciences a lot of recent study has been focused on Relational Frame Theory (RFT), which has had major impacts on effectively treating a range of mental disorders in addition to being used for healthy individuals and sporting teams. Therapies that fall out of this science focus on identifying values unique to the individual, while discarding any attempt to find ones true purpose or aligning ones values to society. I only say this as some evidence of practical applications of a theory that denies objective purpose.
The philosophical background to RFT is contexualism, which our answer may lay within there. This would be where I would go to chase down a better understanding on objective purpose.
And you are right on values in science. I simplified it to highlight a distinction. A classic example is subatomic physics. Without politicians intervening, scientists would never had experimented with nuclear fission, and our knowledge of the sub atomic level would be non-existent. My point however wasn't that.
What makes scientific theories objective? This seems like a red herring, as we're talking about objective/subjective in two different contexts, but I will bite. There is a scientific method and a peer review system which is designed to catch most bias in the scientists observations and logic. Our cognition is known to have heaps of misperceptions and biases, which can lead to subjective 'discoveries'. So we get close enough. I could say more on this subject, but I can't see it's importance to any of you're points.
So in short, I don't think I can properly argue that "there is no objective purpose" (you would need to give me some examples to go forward). Hvaing said that I believe that statement is key to subjective value theorem. Maybe answers to the question: "is there objective purpose in the world?" lay somewhere in existentialism and contexualism, further reading if you're interested.