For wildshape, you retain all class features that can be used in a new shadow therefore you retain you're extra attack from barbarian, as well as the Unarmed defence bonus, because you aren't wearing armor.
However this does not mean you get 3 attacks, because extra attack gives you 1 extra attack, no more, and doesn't stack with other features that give an extra attack, "you cannot make more then two attacks with this feature unless this feature says you do" phb multiclassing.
It does not explicitly state that it does stack with multi-attack, but multi atrack is similar to thirsting blade in that it gives you the ability to have multiple attacks in one turn while not being the extra attack feature. In the phb we know that other abilities that give multiple attacks per turn (thirsting blade) do not stack with the extra attack feature. therefore we can logically conclude that you can use the bear multi-attack option, (with the limitations listed) or take an attack action and gain an extra attack from the level 5 barbarian extra attack ( and do 2 bites) but not both in the same round.