“Are you learning that the Rabanan hold that it didn’t have a din of a menorah at all? If so, why didn’t they just say that instead of saying that it wasn’t wooden, rather tin?”
I would say that is exactly what they are intending to by saying it was “Shpudin” as in Tosfos :הא דקרי ליה שפודים משום שלא היו גביעים כפתורים ופרחים
that the fact that it was Etz l’fi R”Y renders an Etz Menorah as a Menorah and is included in Lo “S,’ so the Rabanan dispute that by saying the Etz then had no Din Menorah as it was only simple Glmy Matchas that are not mekabel Tumah etc..
Again, that is how the above wants to say it (based on the Psikta), simply learning, we would say they are just disputing the fact that it was pure wood..