Which internet solution do you recommend?

Wiki says about this:
The RJ-45 connector [] cannot meet these [Cat-7] specifications due to the tight contact arrangement; all RJ-45 Cat 7 patch cables are a mislabeling (as are RJ-45 Cat 7 network sockets and panels). In order to manufacture network components according to Cat 7, new connectors were specifically designed, which essentially increase the distance between the wire pairs.
That is why I was (and still am) confused, as I want RJ45...

When installing CAT7, to my knowledge there is the possibility to terminate on RJ-45. This has the effect that you only have the bandwidth available that RJ-45 offers - thus CAT7 is by no means fully utilized. The advantage of the whole thing is simply this: Once CAT7 becomes an established standard, you only need to replace the outlet sockets and not the cables as well.

It is correct that RJ-45 connectors do not meet the requirements of Category 7. Therefore, there are no CAT 7 outlets and patch panels. However, there are CAT 6a, which guarantees you 10 GBit/s over 100m cable length. That is "only" the specification. Don’t take it too literally. In practice, cables in single-family homes are significantly shorter and specifications include a margin. Of course, CAT 7 can be terminated with RJ-45. That’s how the whole world does it, even in the professional sector. The advice is to have the better cable installed right away because it costs hardly any extra. Later changing the wiring would be very expensive. This way, you can at least expect to handle the next bandwidth jump. Most people today should be more than fine with 1 GBit/s. Why not, where would the data streams even come from with common internet bandwidths? Sure, there are exceptions, but those are 0.0001% of users. With CAT7, you will be able to easily achieve 10 GBit/s in the future, even with RJ-45 as connector. At least a tenfold increase. After that, from today’s perspective, RJ-45 is definitely the end - at least according to specifications - and other connectors and/or transmission methods will be required. But then the CAT7 wiring will also be at its end, because it moves to fiber optic or other copper media. (For 40 GBit/s, I believe CAT 8 has been proposed as the new standard with a 30m length limit. It seems rather makeshift, but who knows what else might be possible). All these technologies have of course long existed and have been in use for years. But not in the private sector. Because nobody needs it.

I just assume that someone who does not know the difference between Cat 5, Cat 6, etc., will not set up an elaborate home network with NAS, etc. Considering that Cat 6a allows for 10,000,000,000 bits/s and fast internet offers 100,000,000 bits/s, meaning a factor of 100, Cat 6a should already be completely over the top for 99.999% of all users and more than sufficient even for nerds...

I just assume that someone who doesn't know the difference between Cat 5, Cat 6, etc. will not set up an elaborate home network with NAS, etc.

Well, someone who wants a rain shower usually does so in complete ignorance of common or required water pipe diameters.

Well, anyone who wishes for a rain shower usually does so in complete ignorance of the usual or required water pipe diameters.

Well, we are talking about a factor of 100 of what the cables easily provide and what is among the fastest internet speeds available.
If the rain shower lets through 20L per minute, I don't need a pipe that would allow 2000L per minute to describe the conditions...
And even for in-house network traffic, 10 GBit should be more than enough...