<Obligatory IANAL disclaimer>

Fair use in Germany (and the EU) isn‘t really a thing. There are a few special exceptions (mostly for satire and such), but generally these rules apply:

1. If you cover a song (lyrics and melody stay the same), you have to get a license and share the money you make from it with the original author. You cannot be denied this license, but you have to get it before making money off of your cover version.
2. If you rework a song (change lyrics or melody), you have to get explicit permission from the rights holder. In this case, they are allowed to deny you this license. There‘s a pretty famous legal battle running since 1999 (!) between musician Moses Pelham and the band Kraftwerk, because the former used a two-second sample from one of Kraftwerk‘s songs in his work. While a final decision in this matter is still pending, it shows how even very small snippets of music made by other artists might be subject to licensing fees and the need for explicit permissions in the EU.

As far as I can tell, there is no legal way for Suno to just use songs for their product without having a licensing agreement with the respective rights holders.