I'm surprised some low-fee automatic solutions aren't recommended here. Robo-advisors can split your cash across multiple banks on the backend. Using WealthFront[0] as an example, their cash account offers 4.05% APY, and FDIC insurance on balances up to 2M using a ton of partner banks[1] (each with 250k insurance, or 500k for join accounts). It also can send checks, issues debit cards, etc.

[0] No affiliation, other than being a happy customer. https://www.wealthfront.com/cash

[1] https://www.wealthfront.com/cash-account-participant-banks