I have my Vero and Synology NAS connected to my router via ethernet cable but I’ve been having some internet drop outs recently as I believe some work in my area is being carried out.
When the internet disconnects and then reconnects I have to keep adding my NAS to my Vero and scan all my movie/TV files back in.
I believe I would need to setup a static IP address but I have no clue on how to do this.
Does it need to be done via the Vero, the NAS or the router?
yes, that is the recommended approach for proper network setup.
Alternative you can also configure static addresses instead of DHCP on your NAS but that might lead to address conflicts.