Moving the OS is difficult because you would need to reinstall the bootloader which may or may not be easy depending on your skills.

keeping the OS and moving your home is much much easier. as simple as opening fstab and adding a new line entry

(First make and test backups, then) Clone the drive. Then point the OS on the new drive to /home on your old drive. Keep or remove old OS files.

Rsync -rav --exclude home / /destination

Depending on how much customization you have done, it might be easier and safer to just install the OS from scratch to the new disk. You'll also end up in a much more "clean" state afterwards.

• Your program settings, browser favorites, etc should all be stored in /home/
• Your system settings are generally stored in /etc

I would take a backup of the whole system (important!), then take a second copy of only these two folders (save all the permissions and ownership info, and also use sudo to access all the files in /etc !). After you have saved everything, wipe both disks, set them up like you want and reinstall all the software you need. Finally you can restore from these two folders.

You will not want to restore everything in /etc, just the files you have manually/indirectly edited, and also you will need to preserve the correct file permissions, so be careful on what you do there. Some files like /etc/fstab hold the information on how your disks are mounted, so you really don't want to restore those (same for /etc/passwd, systemd units, and many others). Basically restore selectively only what you need, or reconfigure the software again and just restore your /home

It shouldn't take as much time as it sounds, because most of the settings should be in your home folder, and you can reinstall all the software pretty quickly when you need them. You also won't have to fight all the problems if you end up with a weird/incomplete setup when moving the root.