A PC who has died while wearing the Ring of Mind Shielding might be considered an object and a creature.
If you die while wearing the ring, your soul enters it, unless it already houses a soul. You can remain in the ring or depart for the afterlife. As long as your soul is in the ring, you can telepathically communicate with any creature wearing it. A wearer can't prevent this telepathic Communication.
A distinction from other sentient objects to be at least considered would be player agency. I fear my “answer” is just a similar question, but it would be a good candidate for a edge case.
The reason I believe the PC could be a creature is if the DM allowed you to have agency after entering the ring. I believe you would not be considered a Sentient Magic Item. DMG 214
Sentient magic items function as NPCs under the GM’s control.
So in this example you would not be functioning as an NPC and you would not be under the DMs control, so you would have to be something else.