You can be "extremely safe" without FDIC insurance.
For example, a money market mutual fund held at one of the large discount brokerages such as Vanguard, Schwab or Fidelity will pay (currently Jan 2025) up to 4.3% - 4.4% while being about as safe as you can get without FDIC insurance.
Many of the most popular money market mutual funds are invested in U.S. Treasury securities, or securities of other U.S. government agencies that are backed by the U.S. Treasury. They are very safe.
These money market mutual funds are purchased at $1 per share and are intended to remain at $1 per share permanently, though this is not guaranteed. Falling below $1 per share is called "breaking the buck" and it is a phenomenon that has happened only twice in recorded history that I am aware of, once in the 1990s to a small relatively unknown fund that sold at $0.96 instead of $1 and once in the 2008 Lehman Brothers fiasco where one particular fund paid off at $0.97 instead of $1. Additional safeguards are now in place to make a recurrence extremely unlikely. In fact, Vanguard automatically puts cash proceeds from customer transactions into one of these funds unless otherwise requested, so their customers' cash is always earning something, yet remains safe.
The funds pay dividends once per month and you don't have to worry about timing your purchases and withdrawals because dividends are calculated just like interest from the date of deposit to the date of withdrawal.
You can open a brokerage account online at one of the above brokerages and fund your account by connecting the brokerage to your bank. Dividends can be set up for automatic reinvestment, similar to compounding interest.
If you choose online statements, there are no account fees, no transaction fees and no fees to withdraw your funds. Each year you'll receive a 1099-DIV, which works just like a 1099-INT that you would receive from a bank, and dividends are taxed just like interest.
How to choose which brokerage to use? Fidelity's cash management features can't be beat and they have a user-friendly website. Schwab's website is also excellent, and they have good research tools for investors, with excellent customer service like Fidelity has. Vanguard's website is a bit clunky and their phone help is not great, but they consistently pay higher rates than the other brokerages. Since you're not going to be a dynamic investor, but just a boring depositor building up a nest egg, you may choose the brokerage with the highest returns, which has been Vanguard for many years.
I'm not affiliated with any of the above, but I'm a customer of more than one of them.