Higher interest rates favor the savers and disfavor the borrowers. It reduces, first, productivity and, later, consumption. However, I'm not sure there's a strict correlation between those two and bitcoin. Aren't many use bitcoin as savings and/or store of value?

That's true for everything. Food is worth what people are willing to pay for it, gold is worth what people are willing to pay for it, cars are worth what people are willing to pay for them. It has nothing to do with intrinsic value.