I wasn't actually able to find any real documentation on how Synology's SHR works.
Their recovery documentation [0] indicates that SHR is just plain mdadm + LVM and a couple of NAS recovery sites [1,2] indicate the same.
In the end I got a Reddit post [3] with a response from a Synology representative who says that the btrfs filesystem will request a read from a redundant copy from mdadm in order to correct checksum errors.
I wonder whether this is unique to Synology or whether the change has been upstreamed into the main Linux kernel.