That is definitely not a ceramic pot. It is clay and will require lower temperature cooks below the 550 degree range to prevent cracking again. You will also need to start with a small fire to warm the pot before building a large fire for cooking. This is a great pot for low & slow cooks. Also keep it out of the weather because a wet clay pot will crack when it gets hot. Last consideration is the outside temp when firing up the pot. I believe freezing temps will prevent use due to cracking although I wouldn't know about those being here in Sunny California!
Nice job on the fix and paint.
The old clay pots were painted and the new ceramic pots have a baked glaze finish that does not come of and stays shiny and new. BGE is stamp in the dome just under the hole for the thrmometer in the ceramic pots. I am not sure of the appearance of the older BGEs.
Swamprb will be your best source of info on your pot since he is our resident expert.