> TBH, this future frigthens me even more than nuclear war or climate change. For both these old horrors, we at least know the theoretical solutions; but if we simply run out of new things to discover that make a difference for us as a species, what then?

This is very, very unlikely. Take a look at all open questions in physics, and you'll see that our understanding of the universe has severe gaps. Usually, whenever such a gap is filled, there's a technological boom. For instance, Einstein got us some: not only relativity (allowing for things like GPS), but also the photoelectric effect, allowing for (eventually) solar panels. Greater understanding of semiconductors (in no small part due to the above) brought us transistors, cheap lasers, which were refined (and still are) by quantum physics. We are dabbling into quantum computers now.

Mind you, both lasers and radio waves were considered curiosities with no practical applications.

Fusion research is still ongoing. Progress is slow, but steady. Once we have mastered, we'll have access to cheap and plentiful power, which will open up applications previously not even considered before. If it is possible to shrink the technology to less then building sized, then you'll also see vehicles (ships or spacecraft).

Bio technology is still in its infancy. I cannot predict what the results will be, it's far too early.

Some of the rapid progress from the last century might have been an anomaly. But we are not even close to running out of things to learn.