Keep in mind that lot of smaller banks will advertise fairly high rates like 5-6% for a few months and then fall back down to the prevailing rate or even lower

Keep in mind that lot of smaller banks will advertise fairly high rates like 5-6% for a few months and then fall back down to the prevailing rate or even lower (a HYSA with a better return than treasuries is a red flag). IMO better to find a bank that is consistently near the top rate, unless you want to deal with the hassle of moving banks quarterly.