This is a challenge, but there's all kinds of tricks a DM can use to speed one group up and-or slow the other one down.
YEs. But that is extra work, and we should call that out.
It's easier if the same players have characters in both groups, as it becomes in their interest to keep them contemporary.
Then they aren't independent, and we could expect that one will reduce to being an arm of the other, which I don't believe is the intended point here.
I am more concerned with simple continuity.That said, sometimes one group is simply faster than the other, in which case interaction largely comes off the table and the slower group has to accept that they might now and then have to clean up messes left behind by the faster.
Group A raids a dungeon, forcing a tribe of goblins out.
Goblins walk a day, and raid town for supplies.
Group B deals with goblin raid. Sends forces to deal with source of goblins. This takes only two days of in-game-time, but takes a month of real time for various reasons.
Group A should see forces from town show up at the dungeon, but have to not play for a month or have a continuity error.