Recommendations for networking an encrypted OSX Extended format drive
I don't believe an off-the-shelf router or networking device exists that contains this feature.

If you want to do it without connecting it to a Mac, you can use the libfvde program to mount the drive on a Linux system and use that to make it available on the network.

I haven't tried it with a Synology NAS, but as the Synology DSM is Linux-based and allows installing third party programs, it should at least in theory be possible to install libfvde here, mount the drive, and make it available on the network.

You can download libfvde here:

https://github.com/libyal/libfvde