I had this same problem on macOS, where Houdini Engine in Unity would not recognize my Houdini installation, and it had nothing to do with setting a different version of Houdini in the HoudiniEngine > PlugIn Settings in Unity.
The issue was that I had downloaded the HoudiniEngine plugin from the Unity Asset Store instead of using the Houdini Launcher to download the correct .unitypackage.
To fix this on M2 macOS, I used the Houdini Launcher to download the latest version of the HoudiniEngine for Unity and then manually installed it in Unity by choosing Assets > Import Package > Custom Package…. The package was here: /Applications/Houdini/engine/Unity/20.5.332/HoudiniEngineUnity.unitypackage