There comes a point where you are optimizing finances beyond what is necessary, in my opinion.
Have a decent plan for your cash so it's earning good interest, then go out and focus your time on the rest of life. Automate as much as possible. Don't worry about a few $10s of extra interest!
If your bank account is also at your broker (ex. Schwab, Fidelity) then money market funds are actually more convenient than a HYSA. My money market fund money is available the day after I sell and there is no waiting period to transfer between my accounts at Schwab. Also I can use the money market fund to underwrite cash secured puts or for other investment activities.
Transferring between institutions I have had take 3-5 days before funds clear. Wires can be faster but come with fees and a whole bunch of questions to make sure you aren’t a scammer trying to empty an account.
So, it is good to know about all your options. I keep my 6month emergency fund in SNOXX money market fund. With Fidelity you can set a sweep to go into their short term treasury fund and not even have to sell anything to transfer the money out.
There are times when you need to have a ton of money in cash or near-cash (e.g. saving for a down payment for a first home), and then it makes a lot of sense to optimize.
For a normal emergency savings fund, it does not make sense (unless you legitimately enjoy doing it!)
Have a decent plan for your cash so it's earning good interest, then go out and focus your time on the rest of life. Automate as much as possible. Don't worry about a few $10s of extra interest!