The Disco trailer seems to imply that crew was scattered after arriving where ever they ended up. Star fleet seems ceased to exist.
Apparently Burnham arrives in the future some time before Discovery shows up, but she's the only one who's separated from the ship.
Calypso is set a few decades after the era Discovery is sent to, and Craft's people were at war with a culture called the V'Draysh, who idolised relics from the "long ago", including Snow White and a Betty Boop cartoon. Michael Chabon, who wrote the episode confirmed that 'V'Draysh' was a syncope of 'Federation', which suggests stuff doesn't necessarily work out super great in the future.