The classical combo for Polearm Master is Sentinel, for great control of the battlefield (it does not work that often in the many times chaotic battles, but anyway). I would assume the GWM feat does not work as polearms don't have the "heavy" label, but I'm not sure. As Lae'zel left us (only because we killed all Giths ...), our party has a hireling Fighter with a polearm in it, a nice addition to my three ranged chars.
The problem of the Barbarian is that he only gets 3 feats till lvl 12, not 4 like the Fighter. So your ASI is lacking when taking two feats. There is a halberd to buy (tiefling at the inn in Shadowcursed Lands) which adds + 2 Strength, that's an option. Otherwise I use the halberd from Bernhard or the halberd you get in the Gith creche. I don't like the Bear Wildheart Barbarian normally, but for a defensive polearm fighter that might be a good subclass choice.
Multiclassing is not my preference, but I think a Paladin would be a good choice, as you could add a lot of damage to the build with Divine Strike. Rogue Thief might be good too, for more bonus actions.
In the dead tree version of 5e GWM+PAM is kind of an infamous combo but I’ve never gotten confirmation that it works in BG3 especially as you say due to the importance of the « heavy » label. I always liked this as it reinforces IRL superiority of the Polearm on the battlefield.
Your point on feats is well taken. A multi class into Champion or Battlemaster would make sense but I already have 2 other fighter-barbarians in the party :P
