Is saving these Bitcoins exactly the same as investing into a hypothetical basket composed of world stocks + real estate + commodities + ...?
I think yes, because both simply mean storing wealth by forgoing immediate consumption. Then traders should arbitrage away any changes in the demand for money, and this "world wealth index" should flatline. While real wealth increases or decreases, nominal wealth will stay constant. Bubbles in individual markets could still happen, but arguably smaller and/or less often.
Short term credit with negligible risk of default will be available for almost 0% interest rates.
Longer loans will reflect time preferences, which cannot be captured by simply saving cash.
This is an intuitive approach that a fixed monetary base is compatible with optimal economic growth, without redistributive effects.
Bullseye.
This has a nice implication about what is profitable to do. Anything that beats the average return of the economy is worth letting go of money in order to get the resources for. Anything worse than average costs you.