I never seen an issue with going with bigger drive. Not even once in 20 years as I fix stuff.
256 GB is probably because that the BIGGEST that is available out of the box.
File system supports up to 4TB or 147 zettabytes (which is enough for whole internet) depending on what are you using.
If you switch to same size of disc, its easy to copy data over, so OS won't even notice.
if you go for higher capacity, the easiest way is to have another partition for extra space.
if you take smaller than current one, there is some magic to copy stuff like OS.