I'll quote your definition here:
  • a layer-2 is a separate accounting system where the authorization to execute a transaction must be granted by the holder of the account primitive in other words, you can't make a valid transaction on a layer-2 without a valid signature of the party that owns the layer-2 asset. in this sense, coinbase's database would NOT be a layer-2, since anyone who works at coinbase can validly update their database
My problem here is that I think that both WBTC and Cashu are not that different from Coinbase for the purpose of this definition. BitGo could in principle freeze your WBTC, refuse to honor their IOU to you and mint the same amount to someone else, effectively making a transfer. A Cashu minter could refuse to reissue ecash tokens if the request comes from a specific IP - again, the tokens could then be reissued to somebody else. I don't think that these scenarios are significantly more far-fetched than a Coinbase employee tinkering with their database.
In my mind what makes a layer is the number of participating entities. If there would be 100 instances of Stacker News, and they would be all connected through LN, they would form a L3.