Why does infill percentage stop the print from sticking to the bed?
The more infill, the more material. The more material, the more stress is inside the part while it cools down from printing temperature to ambient temperature. Parts with higher infill density tend to warp more (the edges curl up).
But 20 % should be fine, you shouldn't have any issue at that percentage (unless you're printing with ABS/ASA).
I think it's a first layer issue, the 0.2 mm first layer gets more 'squished' onto the bed, thats why you get better adhesion. I'm using PrusaSlicer, every default print profile in PrusaSlicer uses a 0.2 mm first layer, maybe there is something like that in Cura too?
For example the 0.1 mm PrusaSlicer profile will squish a 0.2 mm first layer onto the bed and changes to 0.1 mm layers for the rest of the print.