In most recipes I've found about pressure-cooking pulled beef, the meat is sautéed before the pressure is applied. Why is this? Could I pressure-cook pulled beef without first sautéing it?
Example recipe: https://theblondcook.com/instant-pot-mexican-shredded-beef/
Also, I've noticed there's a lot of similarity between making pulled beef and beef broth. Can it be done in one go?
The reason for steps like this when slow-braising meat is to brown the meat (or, if we're being fancy, to cause the Maillard reaction), which will make the dish taste...more like browned meat. You'll note that in the linked recipe, the sauteing step occurs before the liquid is added to the pot, and emphasizes browning the meat on all sides:
...
Pour oil into your Instant Pot and set to saute. When oil is heated, sear roast on all sides until browned. Turn off Instant Pot.
Pour beef broth mixture and salsa over roast.
...
If you skip this step and throw everything into the pot at once, you'll end up with perfectly cromulent shredded beef. It just won't have the flavor notes of browned meat that would have been introduced by searing it first. Many people (including me) think that the final product won't taste as good without the browning step, but it's not absolutely crucial to the structure of the dish.
I'm answering your second question, which is:
Also, I've noticed there's a lot of similarity between making pulled beef and beef broth. Can it be done in one go?
Yes, you're making beef broth in the process, but I wouldn't add more liquid than the recipe calls for. You want the beef to braise in the pressure cooker as the pressure speeds up the process; you don't want to just boil the beef to flavor more liquid. You're braising because you want that flavor to stay in the beef as much as possible.
With pulled beef, you will invariably have some liquid left over that you can use for dipping sandwiches, or to help flavor your next batch of pulled beef or as a base to make more beef broth, where the goal is to flavor the liquid as much as possible.
Add some of the leftover liquid to a pot that has some roasted beef bones, vegetables to your liking, scraps, etc and some water, and you will be on your way to a great beef broth. Your leftover braising liquid will have given it a head start.
But remember, when making broth, it's all about pulling flavor out of what you put into the pot and putting it into the liquid. When you braise, the point is to minimize loss of flavor to the liquid, and re-introduce whatever flavor you lost to the liquid back into the meal.
So while it's great to use home made beef broth as your braising liquid, or to start a beef broth with some leftover braising liquid, the two tasks are rather exclusive of each other.
