The bug

Although the Piglin now holds weapons similar to a Vindicator, it still uses the player swinging animation which prevents smooth animation transitions.

Special thanks to Latelag in this comment for discovering the bug:

They raise their arms like vindicators but the attack animation is still [that] of a player, meaning their arms [would not] smoothly transition from one location to the other.

The bug relates to MC-186102 which is resolved as Works As Intended.

How to reproduce

1. Use the following command to obtain a strong Resistance effect:

   /effect give @s resistance 300 127 true

2. Use the following command to spawn a Piglin:

   /summon piglin ~ ~ ~ {HandItems:[{},{id:"minecraft:golden_sword",Count:1b}],IsImmuneToZombification:1b}

3. Switch to Survival mode, and then have it attack the player.
   → The Piglin swings its arm similar to a player and then snaps back to hold its weapon similar to a Vindicator.