Monero

Since you're not asking about Haveno, the key question is, what are you trying to federate and what do you mean by localmonero?

This is what I liked about localmonero: (1) It had an easy to use web site -- this can be federated over onion; (2) it had many options (especially necessary if you're not using USD or EUR) -- federation reduces liquidity per mistance; (3) It had a reputation system for sellers -- this is hard to federate; (4) The arbiters have been proven over time to be trustworthy -- this may be impossible to federate without a reputation system.

So, IMO, your first task is to come up with a federated trust system for both arbiters and sellers. Once you have that, listings and trading can happen on any platform, even lemmy or nostr or Simplex or Haveno or something like robosats.

In my simpleminded approach, a wallet public key could have multiple reputations associated with it (e.g. seller, buyer, arbiter). There would have to be a way to confirm that sellers actually "sold" and "buyers" actually bought and arbiters actually arbitrated....I'm sure this could be done in a hidden ZK way by adding transaction IDs to the reputation . Could this be abused since a person can create multiple wallets and trade with himself? Sure, but that could also be done in localmonero and it did fall apart.