I have finally proven that it does indeed regrow roots therefore it is regrowing. Just like with onions. I felt like if it's not making new roots, it's really not regrowing. I needed to see the formation of new celery roots for me to believe it really is regrowing.
The next step is to redo the experiment and see what comes of it in hydroponics or soil. Does it fully regrow or does it just finish growing what was left when it was harvested. I will do at least one more video exploring that aspect. Stay tuned!