Just to confirm what you are saying, you can see the audio connections in Roon’s Settings > Audio on both the phone and PC, but you are not seeing the Zone Picker on the phone at all, just the “Manage audio devices” message?
So you didn’t check your Windows Firewall’s settings?
The reason I asked for this is because, with the last release of Roon, there has been a change to the architecture of the Roon software on Windows setups. The previous all-in-one installation of Roon has now been split up into two components, the Roon UI and the Roon Server. The latter now requires an additional Firewall exception to be made for roonappliance.exe. If that is not there, the Firewall will block any traffic from it to Roon Remotes (including your phone), and this traffic may include the necessary information for Zones to be displayed.