VTP Transparent & PVLAN

I am looking to use VYOS as a routed entity between a private VLAN network.

Does VYOS participate with Private VLAN using VTP-Transparent configuration?

Something like that in the LAB can the VM above VYOS access the private vlan devices down below what configuration needs to be done on VYOS to complete this?

VyOS can do this routing. Since on the router side there is no difference regarding Private VLANs. But on the switch side you need to configure e.g. “Promiscuous trunk port”.
“Promiscuous trunk port—A promiscuous port is an upstream trunk port connected to a router, firewall, server, or provider network. A promiscuous trunk port can communicate with all interfaces, including the isolated and community ports within a PVLAN.”
Private_VLANs
Or did I misunderstand your problem?

Looks like all you need to do is to configure the switch port toward VyOS side the same way as toward Device1
That way all devices will have access to VyOS (and VM). And Device 2 and Device3 will still remain isolated from each other