FDIC insurance is for banks. NCUA is a similar type of insurance for credit unions. For taxable investment accounts, there is SIPC insurance, and I just found out that it also has a limit of $250K per account for cash, but I'm not sure what exactly qualifies as cash, since many people put their "cash" into money market funds, which are technically an investment.
If you want to be super careful, you'd want to check with the FDIC, NCUA, or SIPC to make sure that whomever is holding your money is a member in good standing, but personally I don't worry about it if I'm dealing with a big, reputable company like JPMorganChase, or Vanguard, or someone like that.
Also, I note that the SIPC insurance is only $500K per account total. But it's actually in effect more than that, because that is the amount of losses they will cover if they can't actually recover assets in the event of a loss. I think most big firms have supplemental insurance of some kind to cover larger accounts, but offhand I'm fuzzy on the details. See here for some info:
https://www.fool.com/the-ascent/buying-stocks/articles/brokerage-account-insurance-is-your-account-safe/