Re: So who are these 'veterans' that get invites to the playtest?
First, these are the qualifications for a "veteran" status in the franchise:
"Battlefield Veteran is a rewards scheme for owners of various installments in the Battlefield Series. It is currently calculated by adding the number of all an owner's registered games together minus one. This does not include demos, betas, expansions and booster packs, although they can still be registered for show."
Now with that in mind, it does not automatically grants you an access to the playtest. Like previously mentioned by others - you also have to signup to the EA playtest website. As this is EA's general playtest location and not particular to the BF franchise, you will occasionally get invited to random beta tests of other games. EA also likely granted access to 2042's technical playtest to active Answers HQ members. It also helps if you clocked many hours playing other BF games in the past as it shows you are a true fan of the franchise and not a casual gamer who wants to literally just "play" the latest (vs. testing technical aspects and reporting back with bugs).
/salute.