Let's assume the whole world uses a currency with 100% fixed money supply, e.g. Bitcoin in 2150.

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.

Here's a new idea on how to make Bitcoin (or a future alternative/fork) more sustainable.
The problem is detailed in a number of previous threads and scattered posts, e.g.:
Current Bitcoin economic model is unsustainable
Thought Experiment: Is Bitcoin a Ponzi scheme?

If you don't think it's a problem, either ignore this thread or assume, for the sake of argument, that it could become a problem.
I want to mention that I don't see any immediate need for action, because it does not affect some important use cases, like exchanging your local currency for BTC to buy some stuff. Incidentally that makes Bitcoin similar to your local fiat currency: don't hold more than necessary.

There have been a number of alternatives proposed, e.g. dynamic amounts per block based on user growth or energy costs.
It's not clear which has the most merit, and trial and error would be slow and costly.

The miners are already in charge, because ultimately they decide which client to run. Why not streamline the process and let them vote directly on the best policy?
We can take advantage of the inherent feature of the blockchain as an unalterable public register:

• Each block keeps track of configurable parameters: DIFFICULTY and PAYOUT / block
• Each miner can set them as preferred
• The actual current value, to be respected, is the median of the previous 1000 blocks
  - Even this adaption speed and other parameters could theoretically be made variable
  - Maybe a few more constraints or averaging, so the actual values reflect the broadest possible consensus while still being adaptable

The aim is to enable maximum sustainable user growth, economy growth and protection against double spending with reduced electricity costs.
So, would it work?

Suppose a Bitcoin clone with little to no changes would startup tomorrow. Would miners switch?

I think they would, because early adoptors had (and still have) a big advantage with the current inflation model.
During the first year about half of all currently existing bitcoins were mined, while there were practically no transactions, and almost none of it has been spend.
Why would late comers simply accept this? If you newly learn about Bitcoin, you'll always have an incentive to start from zero.
Unlike gold, bitcoin is not unique and was never intended to be.
I'm not arguing on economic grounds, and do support the austrian school, so please don't restart the old inflation vs. deflation debate.
It's about sustainability of continuous network growth, which seems to need an equal playing ground in time.