or what main mission the BoS embark upon after locking down the Commonwealth
That would imply they have no lined up.
It would take years for them to fully secure The Commonwealth. The BoS's only current mission is to secure The Commonwealth, and track down the remaining synths.
With Both the Capital Wasteland and The Commonwealth under their control, they would control basically all of the upper east coast at this point.
or to make decisions that impact the direction the Institute takes
You wouldn't. The whole point of The Institue questline is based around the idea that you support the Institue's ideas and goals as they are now.
You, as director, as stated by Shaun, only exist to mediate disputes between the other departments, and the departments themselves are otherwise fairly autonomous.
The game makes it pretty clear, you would not be able to change The Institute in any massive way, only guide it on the path they are already on.
or see if a CPG forms again or not
Its been 100 years since the CPG fell, and no one ever tried it since then, and none of the factions want to do it.
it'd still have been nice to know what the companions get up to
Curie, Ada, dogmeat, and Codsworth have no real purpose besides hanging out with you.
-Piper goes on being a reporter
-Garvey goes on helping the Minutemen
-Cait goes on being a fighter(now just without the drug addiction)
-Mccready would go back to his son after his adventures with you are over(as he states),
-X6-88 would go on being a Courser
-Deacon would go on being a Railroad operative
-Longfellow would go on being a guide in Far Harbor
-Gage would go on running the day to day of Nuka World
Do you really need ending slides to tell you that they continue going on doing the jobs they already have?