The latter is not an L2 solution in general. It's just another token, which probably uses the term "L2" to get more hype; token founders need to be more creative nowadays.

You've got it backwards. Layer 2 solutions are long-term. Short-term would be arbitrarily tinkering with the block size, just as many altcoins have done over the years. And that's true, because it's infeasible to have every person on-chain, creating multiple transactions every day, at the scale of hundreds of millions of people, while simultaneously being practically able to verify the ledger.