Anyone have part or all of their emergency fund in an HSA?

I would treat this as nearly the same situation as using your Roth IRA as an emergency fund. This is often only done when you are unable to both max your Roth contributions and save on the side for an emergency fund, so then you keep cash in a money market within the Roth IRA for emergencies.

If the choices are (HSA in cash + taxable brokerage invested) vs (HYSA cash + HSA invested), I think the latter saves a lot more in tax drag.

EDIT: After reading that you are in the 0% LTCG bracket for the near future and your HYSA interest would be taxed at your marginal rate of probably 12%. It could make sense for you to do the HSA in cash + taxable brokerage but only if you can harvest all of the dividends and tax gain harvest consistently at 0% LTCG. This seems like a micro optimization and a short term thing as eventually your taxable account would probably outgrow the 0% bracket.

Heck no. HSA is best used like a Roth IRA in holding the most "Aggressive" (Equity) bits of your investment portfolio, versus as "savings". Tap it before Roth IRA (and death). There are better options focused on Savings (HYSA, etc.).

HSA - The Ultimate Retirement Account

We use the HSA as our secondary emergency fund. However, we're fully invested in the market to maximize the triple tax advantage. For primary emergency fund, we have a years worth of spending in a high yield account and have RE producing the cash flow we rely on.

One downside I see is the opportunity cost of using triple tax-advantaged HSA dollars in the near term instead of letting it grow for many years. Is that cost worth a couple hundred dollars saved per year in tax when you could instead let it grow and later have a larger pile of tax-free dollars? As Ramit Sethi likes to say (a little brusquely), "Stop asking $3 questions and start asking $30,000 questions".

I do a similar thing with keeping part of my emergency fund as Roth contribution basis. But I have a tiered emergency fund, with a few thousand in my primary bank's savings account, a few thousand in safe places like I-bonds, and the rest in investments. The "investment" portion I put in my Roth IRA. I do NOT keep it in a money market fund, because due to the lower tiers I'm not worried about liquidity. I'd recommend the same for you: keep enough liquid that you could reasonably need within a business week, and put the rest in something more profitable.