What Spotify implementation are you using? VolSpotConnect2?
Because if you don’t use SPOP, your phone needs to be able to scan the local network (probably the VPN subnet you’ve configured) to see the client and I presume it will need internet breakout as well (this counts for both the client and your phone).
Spotify (internet) <-> your Spotify client <-> local network scan for device connection option <-> Volumio instance <-> Spotify for playback (internet)
If you use SPOP (the other Spotify implementation), the Volumio instance should just be able to call out to the internet for playback purposes.
The problem could be that your Spotify instance just uses its interfaces’ local network for scanning, and not the tunnel (VPN).
In other news, some googling led me to this answer: No VPN support: Why? - The Spotify Community
And this answer (same, but newer): App not working with VPN - The Spotify Community
In short, Spotify and VPN is not a happy marriage. However… in 2021 I’m not buying this… it should be possible, try turning all protection in the VPN tunnel off for testing purposes on a test machine in a test network! 