You really need to use a hand impact driver to get that out. A good one. Not the cheapest thing you can find (those tear more stuff up than they actually get apart and are a huge waste of money), but one that actual professional mechanics use. The action that they put to the screws is a sharp impact downward on the fastener and a twisting motion at the same time that works to get stuck stuff loose. Here's a link to the type I'm talking about, although I can't vouch for this exact one. Mine came from the Mac tool truck but it looks very similar. https://www.amazon.com/OTC-4607-Imp...ual+impact+driver&qid=1683418555&sr=8-22&th=1
One of these might also work if used carefully. https://www.amazon.com/Shake-Break-Impact-Screw-Remover/dp/B000BHJ7JM
One of these might also work if used carefully. https://www.amazon.com/Shake-Break-Impact-Screw-Remover/dp/B000BHJ7JM