Just sharing our experience - the short version is that I recommend Beak and Barrel for breakfast.
For context, my husband and I recently made our first "just us" trip to WDW. I knew we wouldn't be back for years and I wanted to check out Beak and Barrel even though we aren't big drinkers and I was concerned about the seating (or lack thereof) situation. I decided to make the earliest ADR possible, 10 in the morning, in hopes of a full lounge not pushing us to standing in a sight-obstructed area.
I went to the podium to check in instead of doing it online (after a leisurely MK arrival, a Jungle Cruise LL and a Pirates walk on - day was off to a great start!). I explained it was our first and last-for-a-while visit and that I would appreciate being in the Mess. The CM asked if we wanted to sit and I wasn't going to be pushy, but my husband piped up "yes" before I could say anything. A couple of minutes later, we were taken to a couple of stools. The bar is standing, but at the end towards the door, there is a lower section with two low stools at it. Great spot! Easy to look around the mess and front row seats to the action behind the bar. From the end stool, you can turn around and watch the ship-in-a-bottle battle. People were being put in the standing positions at the bar and seated spots in the Mess and the Captain Quarters. In our 45 minutes, it definitely did not reach capacity. No one was standing along the back wall. A group was put in the Mapmakers room and wasn't in there long.... but I wasn't paying attention.
I was worried about going to a lounge in the morning... but it turned out to be a great thing. The "Island Provisions" made for a great breakfast. (I was thinking we'd also try the veggie Corn Griddle Cake, but didn't.) I had the "Cursed Treasure" drink and was surprised at how much I enjoyed it. (The cookie crumbs are in the beverage- the texture could be off putting to some.) I ended up drinking two! My husband ended up indulging in some rum. I think he was inspired by the heavy theming
We stayed for our entire 45 minutes. Between the drinks and the provisions, we left quite satisfied having had a relaxed, fun and filling breakfast.