What are the risk types for a large amount of savings in an index fund

What is the purpose of the savings?

If this is an emergency fund, savings used to protect against short term negative happenings on your life, then there is a real risk of prices being depressed when one needs it most. For example, the economy tanks and you lose your job and are finding a difficult to fine another one. You need money until things improve. During such times, the stock market is down sharply. You don't want to sell at that time.

For this kind of account low paying savings accounts or government bonds work best. It sucks, but think of it like insurance. You pay for home owners and car insurance, but the prices are worth it. For emergency funds you pay a price in opportunity costs, but it is worth it.

If the savings has a much longer time horizon, then there is no need to be concerned with short term fluctuations. Lets say this money is earmarked to buy a retirement property. During your time, you may see massive dips but the only thing that matters is what is the value at the time of property purchase.

Even then it is easy, do you hold off and wait until stock prices improve, or do you buy now anyway because maybe real estate prices are also depressed? You could also do a partial withdrawal, taking some money out for a down payment, but then getting a mortgage. Once prices improve you could then pay off the mortgage. A lot of options.

The only risks are market risk (which you already mentioned is not something you care about), and provider risk (which is essentially nil).

Big providers like State Street or Vanguard are not going to go under any time soon, but if they did (or if they decided to stop managing a specific ETF/fund, which is far more likely), there would be a liquidation process whereby you would be entitled to your percentage share of the fund in the individual stocks making up the fund.