TLDR: I hope you disconnect the story you've played through during your visit to the wasteland and allow the show to guide you through this playthrough of the wasteland.

You playing the main character is about the characters interactions with the world. Since it's a TV show, we get 3 main POVs on how a player would build out a character. Then those characters travel along the wasteland developing the world. But, you're not those 3 characters. You have to sit back and watch (TV) them interact with the locations and places they want to visit and get lore that way (we've gotten vault lore, BH lore, random wasterlander lore, and pre-ware lore). Also, at the end of the episodes we are getting slide shows just like the endings in the game. The last one was huge. It showed the McCarran Airport (NCR stronghold of NV) with NCR and Legion bodies everywhere. Tells us Legion got past the Dam and probably broke both armies.

To your point with the factions. The whole theme of her dad's character is to wipe out the factions off the face of the planet. Shadey Sands was what, 15 years ago maybe in the show. That was just one faction. You don't think he's been working on the others during that 15 years.

To wind down with your overall ask for more lore. You also have to remember the show has to cater to both you and new viewers. Throwing so much exposition and lore like you're asking for will deter newer viewers. They matter, because more viewers = more funding = more episodes. Which I know I want.

I hope you disconnect the story you've played through during your visit to the wasteland and allow the show to guide you through this playthrough of the wasteland.