You create a new raid array with the two new disks and move the data there?
I fear you'll have to be more specific about what doesn't add up for you...
I have the whole OS on that RAID.
Should I just create the new MD and copy everything there? I guess that I need to copy data when the OS is shut down (so with another PC), correct?
In your shoes I'd do just that (booting from a usb stick and creating/mounting the appropriate partitions in the new drives)... but you might find resilvering or resizing partitions easier if you are more familiar with those operations that I am.
It must be said that actually copying the files rather than working with block devices will let you switch to a different filesystem (or take advantage of updates/optimizations recently introduced by your filesystem) or use different mount options (eg. add compression) and should in theory lead to better performance (eg. less fragmentation). In a homelab the performance difference will probably be unnoticeable anyways so... just go with the method you are most comfortable with :)