Higher yields are possible with various different investments but they all come with additional risk. You do not want to have an emergency fund they may drop in value during a period which you may need to draw on your emergency fund, such as a market downturn that leaves you unemployed.
Similarly, you want to be able to access emergencies funds quickly. Emergencies are generally unexpected. If you need to wait for funds to unlock or for sales to settle, then it could possibly be too late.
In that case, I do not believe there's any options that are better than a savings account in terms of reduced risk and immediate availability of the money when needed.
In theory, you could say that a higher return is the risk premium you demand. Turning that around, higher returns means the product is more risky, and thus a bad fit for an emergency fund. Even with inflation a lot lower in the past years, a savings account still didn't exceed inflation in terms of return.
Traditionally, stocks have been a good hedge against inflation, but especially in the current market there's a lot of volatility which is not a good fit for emergency funds.
I have personally reduced my emergency fund to a level I'm still comfortable with, with the rest of my savings in investments. And frankly, my emergency fund is just a small part of my total net worth, it's OK if that part loses some purchasing power over time because it's optimized for other goals, like immediate availability, and a more predictable loss of value over time.
Stocks are not a good option obviously. Current situation is a testament of that. We can see the situation in Russia now where the stock market itself is shutdown (obviously these are exceptional circumstances) but people loose total control over their investments for unknown period of time.
That said, these troubling times are even more riskier to invest. Perhaps, the best you could do is to prepare for potential supply chain issues with gasoline, LPG, etc.
I happen to stay in Sri Lanka nowadays, where the inflation crossed 16%, and the there are many issues with lack of essentials. Supermarkets don't sell more than 5kg of sugar, me having to drive 20km because the three gas stations I drove past didn't have petrol, and soaring prices of pretty much everything.
I thought to stock up the essentials to last a couple months or so, expecting the imminent worse conditions.
In Europe, though, I don't think things to get this extreme, but my suggestion would he to stock up. Not hoarding piles of toilet paper, but make sure to have a reserve can of petrol, extra medicine, and the essentials to last a month or two. Food prices went up about 20% in just last month here, and that annualized return of 240% I'd much better than the appreciation of gold, real estate, stocks, etc.
I think the advice also depends on your own personal scenario. In my case - I have to save extra money on top of 401k, Roth IRA, etc. in order to retire. (Social security plus that isn’t anywhere near enough) So, can use that brokerage account as an emergency fund as well. Which is more or less what I do now, tbh. The assets are all mixed. It’s mostly irrelevant.
I still keep 20k cash in my account but I try to not keep more. (Sometimes I have $10k bills in a month or what not - like having the buffer and like being able to divest an entire month or two of paychecks to just do all 401k in that time)
I can recommend to anybody who ownes stocks to ask your bank about such a line of credit, because it has no costs as long as you do not need the credit, but if you need money you can immediately draw a flexible amount of cash for exactly the time you need it.
I created an account this week with https://beta.getquantbase.com/
I have not invested yet...
I think younger folk or those in a less financially secure position could be better off holding cash rather than investing their fund, but those people will also have more frequent use of an emergency fund (i.e. an emergency to a young person could be significant car repairs of $1500 where someone who's 25 years into their career could more likely take that in their stride)
So basically, my cop-out is "it depends" but as a rule of thumb, stocks are normally ok during inflation as you are owning a slice of the economy that is undergoing inflation.
The best security against economic changes is to try to keep a large gap between spending and earning; I think the question of "where to put your rainy day fund" is then less relevant.
Everything that is not an emergency fund is in stocks/etfs.
Do your research on which is the best yielding. In Australia, at least when I last checked, it's LFSPA.
Obviously these must have gotten more expensive since inflation rose. But it will protect you against higher inflation. You'll lose in case of deflation/lower inflation.
Be sure you understand the product before getting into it.
Probably not the solution you are looking for, but it should work...
Otherwise, I don't know.
To be honest I am seriously considering a move to say South America. Even if we don't end up in a hot war, the persepectives for freedom in Europe are very bleak.