Epistemic status: I don’t know much about the subject. The following is stated much stronger than I believe it.
The market consists mostly (I assume? Please correct me if I’m wrong) of quants and traders trading for other people’s money. Either rich people or pension funds. If the quants can make good trades by buying stock that will increase and sell stocks that won’t, they will be rewarded. Hence, such trades are incentivised and we should expect the EMH to hold between stock prices.
However, no one is really incentivised to tell the owners “look, I think the world is going to end soon, you should just spend your money instead”. If the world was obviously going to end soon, some financial advisors would say so. But no quant will be paid to try to find out if the probability of the world ending is 1% or 10% to find out if the client should spend their money now. So we should not expect EMH to hold for interest rates.