You're on the right track but it's not the moves that are banned, it's that specific Bronzong itself. What I mean by that is that the ranked ladder bans any Pokemon that doesn't have the Galar symbol in the summary screen, which means that the Pokemon needs to be caught or bred in SwSh itself (This means that stuff like Terrakion is also banned, who would normally be legal).
This effectively bans move combinations that require transfer from previous gens, but moves like Knock Off, Stealth Rock, and Toxic are fair game as long as the Pokemon can actually learn it in SwSh. In this example, Bronzong can learn Stealth Rock since it's a TR, but it cannot learn Toxic without transferring it from a past gen.
As a side note, there are some abilities and Pokemon that aren't obtainable within SwSh normally, but those are still allowed because you can just breed that Pokemon in SwSh and it will have the Galar symbol, such as Unaware Clefable and Primarina. Alolan Raichu and Kantonian Weezing are exceptions here though that are still banned, because at this time Pikachu and Koffing only evolve into the other form (maybe DLC changes this though).
This effectively bans move combinations that require transfer from previous gens, but moves like Knock Off, Stealth Rock, and Toxic are fair game as long as the Pokemon can actually learn it in SwSh. In this example, Bronzong can learn Stealth Rock since it's a TR, but it cannot learn Toxic without transferring it from a past gen.
As a side note, there are some abilities and Pokemon that aren't obtainable within SwSh normally, but those are still allowed because you can just breed that Pokemon in SwSh and it will have the Galar symbol, such as Unaware Clefable and Primarina. Alolan Raichu and Kantonian Weezing are exceptions here though that are still banned, because at this time Pikachu and Koffing only evolve into the other form (maybe DLC changes this though).