Equipping armor via right clicking will play the hand animation accordingly, but performing the same action directly via the inventory will not display such an animation.
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May be intended due to @unknown:
"Having no animation is consistent with other inventory actions, e.g. repairing an item on the anvil"
Can confirm in 21w05b.
Can confirm in 21w06a.
Can confirm in 21w11a.
Can confirm in 21w14a.
Can confirm in 1.17.
Can confirm in 1.17.1.
Can confirm in 1.18.1.
Can confirm in 1.18.2 and 22w18a.
Can confirm in 1.19.
Can confirm in 1.19.2.