So my guess is that:
Koby defeated one of Boa Sisters and then Hancock took him down
BB arrived with his Fleet which made Fujitora and Buster Call retreat (Koby stayed)
SSG is Vegapunk's Version of Raid Suit given only to certain Individuals such as Smoker, Sentomaru, Lucci ... etc
Koby used it but it was still not enough against Hancock due to her Adv. CoC. Her Bounty is above 1.5B
BB Commanders take multiple Kuja as Hostages, BB asks Hancock to work with him (He wants to use her to be allowed entry to Elbaf Kingdom, but he told her that Luffy is captured there after seeing his Huge Poster and knowing she didn't receive Wano News)
Koby (Presumed Dead) is spying on them and decides that Alliance between BBP and Elbaf cannot be allowed, and knows Marines won't help with Elbaf, just like Wano, so he decides he must contact SWORD Leader and tell him he is going to Elbaf