Make sure you compute exactly how much money you'll earn from switching with how long you'll likely stay put. If you'd stay put an entire year and only earn $20, is it worth it?
Rather than chasing the absolute highest rate, I prefer to choose a bank that is regularly competitive. Ally bank, Betterment, and Wealthfront are all ones I'd consider. Alternatively, you can use a money market fund at a brokerage. Those react very fast to interest rate changes and are higher than any bank I know of right now, but have basically been 0% in the past while banks paid up to 1%.
You should not be looking to make decent money off your HYSA - just take some sting out of inflation for short or medium term goals. To make money in the king term, you need to take more risk and invest.