Fallout 4 The Minutemen Side quests become available when you don’t work with other factions and pledge loyalty to this one. You will face The Institute and Brotherhood of Steel at certain points.

Fallout 4 The Minutemen Radiant: Recruitment quests are available at different settlement. People will ask for your help with various matters such as kidnapping, enemy threats and more.

That means it was not destroyed as it was in some of the Fallout 4 endings. That leaves a few options on the table, namely the Minutemen and Brotherhood of Steel endings for the game, but likely ...

The Brotherhood airship seen in the show has been confirmed as the same airship from Fallout 4, meaning either the Brotherhood wiped everyone out in that game, or the Minutemen ending was used ...