A few days ago, I started fooling around with the JetBrains IDEs, such as loading a Unity solution in Rider for Unreal Engine and see how it behaves. But then, I noticed that in there, in the case of serialized member variables, it marked a warning that said they do not match the private instance field naming rules.
Anyway, I thought this was one of the consequences of doing such thing, so I went back to Rider and noticed that warning was still there. I headed to the settings and made sure the inspection for the serialize field naming rules was enabled, and it was, but it is not working. I even tried changing things like the prefix or the suffix and the rule itself, but it still remained taking the variable as a common instance field.
Also, I set the external default editor in Unity correctly and made sure the plugin for the Rider support in it was up to date.