How to Find Missions after Main Story Complete?

I'm not much of a gamer, but my daughter and I have played through both Borderlands 3 and now Borderlands 4 together and it's a blast. We completed the main story in BL4 intentionally bypassing most of the side quests along the way. Intent was to finish the main story, build our characters out (we're levels 42/45 now) and then go back and keep playing doing all the side quests.

But it seems like it's hard to find side quests and most of them are really easy. We're just using the Map to scroll around and look for things to do, but feels like there has to be a better way. Also, last night we bought the Vault Hunter Pack but it doesn't seem to have done much (I can see the new C4SH character available, but when we try to create one nothing happens).

I feel like we're missing some fundamental mechanic of how to locate and complete missions once the main one is done. The Missions page always shows nothing now. We also ended up in a spot the other night (sorry, can't remember the name of the place) kind of a city environment where we found a huge door that looked like it led outside the city but it was locked. It looked like there was a bunch of missions behind it, but it said something about DLC required. Not sure which DLC we need.

Anyway, sorry for newb question - we just want to keep killing and looting but aren't sure where to find specific tasks to do. Thanks for any help pointing us the right direction!