Have a Nintendo Switch as mentioned above.
Now I would like to play a homebrew software to have more options.
Is there already an exploit for a patched switch on firmware 9.0.1?
Is there, yes. I have too. But homebrew only goes on an unpatched switch.
Enter the Internet: "Is my Switch CFW capable - check serial number"
Since you come to a page where you simply enter the complete serial number. If the result is green, you can install a CFW. If it is yellow you can try it and if you have red you have no chance.
If the result is green or yellow, just type in google: "Install Nintendo Switch Atmosphere CFW 9.0.1". Then you will find a guide for it.
You will need a Jig and at best a dongle. These are available for around 10 euro on Amazon and co.
Thanks, yes I've already been so far. Unfortunately, I have a patched unit, quasi red. Is there still no solution in this case?
No, in the case only helps sell and get a used unpatched, because the patched switch can only flash up to firmware 4.0.1.