The problem with the Boycat app is that it goes too far and lists EVERY single company (which is not a problem if you want to make sure you’re not supporting genocide). However, this ends up being overwhelming for the average person. The point of the BDS movement is to have material gain through collective action via targeted boycotts. That’s why the list is so small.
They’ve been taken off the list after they withdrew as a sponsor for the Israeli Football Association - BDS got the result they wanted. It was the same reason that Puma used to be on the list. Reebok now has the contract with the Israeli Football Association which is why they are a priority target now.
As far as I know, Starbucks has never been on the list. It was just a grassroots campaign that got a lot of attention and was never fully endorsed by BDS.
This list is all the companies. It’s mostly American companies. There are no British companies on the list that I’m aware of.