HYSA, switch or stay?

Tldr: Does it really matter make a difference to move my money from a 3% HYSA to a 4% HYSA if I like the simplicity and continuity of my current?

I have an AMEX HYSA which I’ve had for years now. It’s currently at 3.1% interest rate and I think when I first got it was upwards 4%. Should I move my money into a higher interest rate acct or is the hassle not worth the extra 1% gain?

For context, all of my money is in my brokerage and retirement accts. I intentionally keep about $5-10k in my HYSA but usually don’t even need to touch it bc my monthly income covers my monthly expenses and the rest gets sent to my brokerage. Retirement contributions are automated.

I’m in the military so, although nothing is ever certain, I have more surety than most that my income will remain the same so I don’t feel the need to have up to 6 months of expenses in my savings. I also have a monthly $4k that comes in on the side that I just automate to my brokerage. So worst case, I’d use that the supplement an emergency.