Nintendo Switch flickering blackscreen repair?

The whole thing started: I played with my switch in TV mode and every few minutes the picture was black for about a second (the HDMI signal always breaks off for a moment). The next day I use the switch in two other TV docks. Had no problems. But when I got home and used it again in my TV box, everything was fine at first, but after a few minutes it started again. And in ever smaller intervals, until after about a minute, the picture was completely black. I plugged in all the cables, tested it on another TV and still the same problem. And always the same pattern that it starts just after a few minutes and then becomes more and more. I thought it was because of the TV box, the other was finally. So I sent her to Nintendo for repair. Now I've just used another TV box and got a big scare when it started again after a few minutes. So it has to be on the switch. If you send it to Nintendo, it will be formatted and I really do not want to lose any files (eg 85% in BOTW) … Does anybody know a solution how to fix them and if not, a way also the data of games How to backup Splatoon or Pokemon Let's Go that does not support cloud backup? Synonymous have a Micro SD, on the screenshots, etc. Are on it.

Have you ever changed the HDMI cable?

Yes, I have changed everything in the meantime. HDMI Cable, TV, TV Dock… And the problems are always the same. I thought it was on the dock, but it does not. It has to be on the switch…: /