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Then why do we still search for a solution for long-term storage e.g. in Germany

Because the Coal lobby in Germany currently controls half the Parliament. There is no 'search for a long term storage solution.' There is a 'lets immediately shut down all proposed long term storage solutions with no actual reason given.'

Germany's parliament has rejected:

1. Burying Nuclear Waste.
2. Building new plants that can use existing waste as fuel.
3. Paying countries that do Bury or recycle waste to handle the nuclear waste.
4. On-site long term Caskets.
5. All long term space related exploration, and thus all space related nuclear solutions.

This isn't 'searching for a solution,' this is 'coal money is more important than actually doing anything.'

Like all the barrels we just threw into a salt cave and broke open over time are now really expensive to retrieve

You mean the barrels that the IAEA didn't approve for the environment Germany stored them in and were not recommended for long term off-site storage at all? The ones that Germany's nuclear oversight agency chose despite international and industry warnings?

Weird how that didn't work out for you.

We’re talking about time ranges, that are just too long for us to handle safe storage

Non-Portland-Concrete encased Titanium and Lead alloyed caskets have an average estimated decay lifespan close to the decay time of the sun, so no, not really.

All the stuff we hear about usage of waste - to at least make the waste of that a bit easier to handle - is still just experimental

It's actually not. Recycle reactors have been in use in China for close to a decade now, there's at least one commercialized product ready to be deployed in the US, and if the Amerisraeli empire would stop bombing Iran for two fucking seconds Iran's main design uses low grade uranium which would allow a 'second life' to most disposed fuel from western designs with minimal enrichment.

Edit: and needing to shut off reactors, because it gets too hot, doesn’t really sound future proof

There is not one singular type of nuclear reactor. Molten Sodium reactors do not have this problem. Heck just more modern reactors in general don't have this problem. Fun fact did you know there are geothermal cooled reactors? Seems like a perfect solution there.