List of interactions
The following interactions should play the hand swing animation, but currently do not:
Modifying equipment on an armor stand
Using a lead on a mob
Using a name tag on a mob
Feeding a mob its breeding item (baby/adult)
Feeding a mob its taming item
Feeding a dolphin fish
Feeding a baby mob to grow
Feeding a brown mooshroom a flower
Using a dye to change a mob's color/collar color
Shearing a sheep/mooshroom/snow golem/beehive
Feeding a golden apple to a zombie villager to cure it
Milking/souping a cow/mooshroom/goat
Commanding a pet to sit or stand
Interacting with redstone ore
Accessing a chest/hopper/command block minecart
Starting to ride a pig/horse/boat/minecart/strider
Catching a fish/axolotl in a bucket
Attaching a chest to a donkey/mule/llama
Accessing a horse-type mob's inventory
Giving bamboo to a panda
Giving a cookie to a parrot
Using a saddle on a pig
Initiating a trade with a villager/wandering trader
Bartering with piglins (Clicking the Barter button on Android/right-clicking on Windows 10)
Using a carrot/warped fungus on a stick while riding on a pig/strider
(Only on Bedrock) changing armor stand pose
Equipping armor by right clicking
Repairing iron golem with iron ingot
(Does not include all interactions that exist in Java)
Related issues
is duplicated by
relates to
Comments

I'm pretty sure that at least some of these are working as intended

[MCPE Helper] LateLag Probably, apart from the punching/mining animation when punching air, which works as intended in Windows 10.

can confirm that the arms aren't swing properly and switching from left to right at times when punching or eating.
Updated the report to include several more cases that I have found. Hope you don't mind.

List of Interactions that do work.
Throwing items
Throwing splash potions/snowballs/eggs/ender pearls/eyes of ender
Using a fishing rod
Punching air (Only works for Bedrock Windows 10 Edition)
(List may be incomplete)

[[Helper] LateLag|https://bugs.mojang.com/secure/ViewProfile.jspa?name=LateLag] As far as I know all of these actions play the hand swing animation in java edition.
Some of the animation are fixed in Java 1.16-pre1:
Entering a boat
Shearing sheep wool
Feeding brown mooshroom
Feeding baby strider to grow

I think changing the pose of an armor stand is also supposed to play the hand animation. Mounting an entity should also be added. On java it plays when mounting.

Affects 1.16.100
Affects 1.16.200.56 Beta

affects 1.17.0.56

Affects 1.17.40.20

Affects 1.20.10.21
Added:
Repairing iron golem with iron ingot

Relates to MCPE-98178.
Also, punching the air doesn't have animations, but it still play a sound. (Tested only with Android using touch)