As High Yield Savings APY continues to drop, at what point do you start considering moving some of that money to a different type of investment?

I keep $60k in my HYS as an emergency fund. Any money of that that accumulates based on the APY, I reinvest into my brokerage account. As of 5/15/24 the APY was 5.15%. Now is has dropped to 3.8%. Just wondering if some of that money should be sheltered elsewhere other than a HYS even though it's an emergency fund.

Thanks!