Direct experiments on the earth's surface tell us that the earth is accelerating upwards.
The OP and the relevant wiki articles all frequently and approvingly refer to the Equivalence Principle when discussing UA, but the EP states that acceleration of the Earth and gravitational acceleration are experimentally indistinguishable. How then can experiments on the Earth’s surface tell us that it’s the Earth physically accelerating upwards, not gravity pulling us towards Earth?
The OP has some explaining to do before rubbishing general relativity.
The problem is that you read a sentence about gravity from physicists and think that it's talking about Newtonian Gravity because that is the topic in dispute here. Those the same physicists also say that General Relativity succeeded Newtonian Gravity long ago. The gravity they are talking about is General Relativity. They are saying that upwards acceleration of the earth's surface and the General Relativity theory of gravity are experimentally indistinguishable in laboratory experiments. You will also find that those sentences of indistinguishability appear in articles about the history and advantages of Einsteinian gravity, giving additional context to which gravity it is talking about.
Remarkable. I'll be blunt then,
which experiments on Earth's surface tell us it's the Earth physically accelerating upwards, not gravity pulling us towards Earth?
Your difficulties with Brian Cox are at least partly accounted for by his mischievous nature – in the original video you referenced, he's already mocked people calling him a paid NASA shill by claiming that's how he can afford to stay in the Raffles Hotel, Singapore, lol. General Relativity builds on the work of Special Relativity by developing a means of relating different frames of reference where acceleration and/or rotation are involved. The mathematical methods of accomplishing this are indeed very high-level, but they allow us to consider a reference frame with the Earth moving upwards through space
if that suits the case we want to analyse. Cox and others enjoy provoking the viewer's interest by citing just such a case, as well as having a dig at those who believe the Earth is physically accelerating upwards. Protesting about "metaphysical mathematics" only shows no appreciation of the breadth and scope of the subject – it's beyond my pay grade too, but you might at least try. On the other hand, UA is easily dismantled with some experimental evidence and schoolboy physics.
Should anyone's interest be piqued, Einstein himself wrote a more accessible book on both SR and GR.
https://www.ibiblio.org/ebooks/Einstein/Einstein_Relativity.pdf