thanks for your suggestions. My project resolution is 1080x1920px, stretch mode "2D", aspect "keep".
Disabling font oversampling got things rougher, as you mentioned, but actually enabling "Use Pixel Snap" fixed the problem. With that, everything looks just fine.
(Error7Studios on Reddit suggested this - I'm usually asking my questions there as well.)
I just realized that "Use Pixel Snap" leads to animations not running smoothly anymore. Zooming a sprite, for example, then "trembles, jitters, bumps" around a bit...
I tried playing around with Rendering and Display settings like Dynamic Fonts Oversampling, Stretch Mode 2d and viewport, but nothing really helped. The weirdest thing is that if I set the scale of my Label not to 1 but to 1.001 (x and y) suddenly it looks good! Now I don't know what to do... is this a bug?
And EDIT continued:
It's getting weirder and weirder. It appears that only the even-numbered lines show the distortions, but not the odd ones! (I tried Label and RichTextLabel with several fonts.)