Barbarians should still be able to apply their Rage damage to Unarmed Strikes. They technically deal 1 damage, but that 1 damage is treated as a D1, as confirmed by the Player's Handbook's wording and backed by Jeremy Crawford. ie. Unarmed Strikes count as weapon attacks, but fists do not count as weapons.
Technically, it should be working as follows:
1D1 + 3 (16 Strength) +2 Rage bonus
6 Damage per hit
Obviously not the ideal way to play, but thematic at the very least.
In addition, Frenzied Strike in-game currently states "As a bonus action, make a melee attack
with your equipped weapon, dealing Weapon Damage slashing damage.".
This should technically say
"Make a melee weapon attack", as in
any kind of melee attack, not specify that you
must have a weapon equipped.
The PHB also states "Starting when you choose this path at 3rd level, you can go into a frenzy when you rage. If you do so, for the duration of your rage
you can make a single melee weapon attack as a bonus action on each of your turns after this one."
A melee weapon attack
also includes Unarmed Attacks, as seen here:
https://twitter.com/jeremyecrawford/status/1088200198814232577?lang=enThat means that Unarmed Strikes should be
A ) Able to use their Rage Bonus for additional damage
B ) Able to be used with Frenzied Strikes
On top of this, seeing as the Berserker already has the trait of "you deal extra damage with improvised weapons" and Tavern Brawler includes proficiency with said improvised weapons (Which I don't believe makes a huge difference in BG3), I would love to see Tavern Brawler increase Unarmed Strike damage to possibly a D6 rather than a D4. Then, you could play something along the lines of the following:
Unarmed Attack
1D6 +3 + 2 = 1D6+5 damage per hit
Unarmed Fighting Style would also be nice, but it's sadly not PHB content.
Alternatively, some gauntlets that increase Unarmed damage would be cool too, but I'm hoping for something more like the above fixes to make it part of the "base" part of the character, rather than an item.
Sorry for the long post! Just very enthusiastic about being able to angrily punch and throw some goblins around!