You’re overthinking it. Sommers was just letting them know what group he is a part of, because they were going to be assimilated by force into the WG anyways, so secrecy didn't matter anymore
Do you people even understand what secrecy is? Nami didn't know who Shanks was despite being a yonko, don't mean him or the yonko existence are kept secret by the WG.
Just the fact one of the HKs jobs is to conquer new territories for the WG goes against the very notion of them being secret. They're literally an assault force, not some secret agents. They just rather kill civilians than face pirates lol.
You're hateboner for the admirals truly make you retarded sometimes