Replace one disk, let the raid rebuild. Do the same with the other disk. Do an mdadm grow, then maybe fdisk / lvm / resize fs depending on your setup. Don't forget to install a bootloader when you put a new disk in.
Making a new array and migrating data is for chumps.
Oh, so easy?!
If the RAID rebuilds the disk, why should I install a bootloader? Isn't it already in the rebuilt disk?
By the way...hemmm...how do I install the bootloader? 😣
Yes it's really that easy. Raid in Linux is usually at the partition level, not the whole device. The bootloader resides in the first few blocks of the disk before your partitions, and isn't included in the raid.
Use grub-install on the new disk device, ie /dev/sda
If you have enough drive bays, I'd probably shutdown the server, live boot into any linux distro without mounting the drives, then use dd to copy from 1st 256GB to 1st 500GB, from 2nd 256GB to 2nd 500GB, then boot the system, and use resize2fs to expand the file system to fill the partition.
Since RAID1 is just a mirror, the more adventurous type might say you can just hot swap one drive, let it rebuild, then hot swap the other, let it rebuild again, and then expand the file system all online live. Given it is only 256GB of data max, on a pair of SSD, it shouldn't take too long, but I'm more inclined to do it safely.
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 :)