The Unarmed Fighting style from Tasha's states:
Your unarmed strikes can deal bludgeoning damage equal to 1d6 + your Strength modifier. If you strike with two free hands, the d6 becomes a d8. When you successfully start a grapple, you can deal 1d4 bludgeoning damage to the grappled creature. Until the grapple ends, you can also deal this damage to the creature whenever you hit it with a melee attack.
Would a, say, 2nd-level Monk gain a benefit from taking a single level in Fighter, making unarmed strikes with a d8+STR? This seems better than the 1d4 from the early levels.