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 @unknown 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
Use the following command to obtain a strong Resistance effect:
/effect give @s resistance 300 127 true
Use the following command to spawn a Piglin:
/summon piglin ~ ~ ~ {HandItems:[{},{id:"minecraft:golden_sword",Count:1b}],IsImmuneToZombification:1b}
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.
Duplicate of MC-187031 which should relate to MC-186102 instead.