When I changed the parent type of MyNetworkManager from MonoBehavior to NetworkManager, Visual Studio did not underline it.
Intellisense did not know about Mirror.
This might have had to do with the history of Visual Studio on my PC: I installed Unity, then uninstalled VS2017 and installed VS2019.
I found the solution here: https://forum.unity.com/threads/intellisense-not-working-with-visual-studio-fix.836599/
It comes down to going into the External Tools Preferences in Unity, selecting the correct version of Visual Studio and making sure that csproj files are generated for (inter alia) registry packages.