Yo Einar, it's the rolling shutter. Jello effect. There is not much to do with it, you can however remove the jello effect almost completely in Premiere if you only move it one direction, ie. only pan or only tilt. Remember we played around with it in Saaremaa with my A6300?

The thing is that the bigger sensor you got and if it's 4K then the cameras lack hardware capabilities to keep up with fast movements. GH5 has a smaller sensor and that helps.
An other thing you can do is film in 1080P on your A7sII, then there is virtually no jello effect. :)