How would I go about expanding my root partition?

Typically you boot from other media and go loose on the drive with gparted.

If your NAS is a PC then you can prepare a thumbdrive with some linux desktop distribution that supports running from a thumbdrive. Most popular do.

If it is a headless device you may prefer to move the drive to another Linux computer (or windows computer booted from a thumbdrive) and do the deed there.

The process typically involves making one other partition smaller and moving it. Followed by expanding the root file system. The first step may be skipped if there are no other partitions than the rootfs.

However, I suspect that you are doing something wrong if you need to resize the rootfs. You use it for other stuff that it is not good to use it for. Storing media metadata, databases, docker images, home folders or other stuff that better should be stored on the data partitions.

The reason for this is to simplify backups and upgrades. With a small rootfs it is easy and fast to image. And you only have to do it rarely, after significant changes. Data need to be backed up much more often and typically using some other method than whole partition imaging.