The ph of your final product should be 4.6 or below for it to be shelf stable. You can get a ph meter and experiment at home and when you are confident about the ph, send it to the food lab to get the ph tested. Once you have it certified from the lab, you can hand that over to the department of agriculture. The will certify you and get plan review or ...
An unglazed ceramic vessel should help to regulate the moisture issues that many of the others have mentioned (which would be true in a glass jar).
Glass jars are also problematic as they act as small greenhouses, with the light warming the jar which can cause it to spoil faster.
I would recommend that you fit what garlic you can into the container as ...
No citation, so not a 'real' answer; but common sense would say, "It's got air holes & it's dark" which makes it better than a sealed jar or glass jar.
Whether it's better than the cellar, outhouse or salad crisper in your average modern fridge… well, it looks pretty ;-)
Breaking them apart to put in a jar - I see several issues.
You will almost certainly break through the skin on a good percentage of them as you separate them into individual cloves, meaning they will have lost their protective layer.
Unless the jar has some kind of desiccant, there is potential for the garlic to sweat & go off rapidly. The air inside ...
Traditionally (at least in Spain) garlic was kept in a braided string, hung in a dry place, so that they could last until the following season.
Separating them in cloves will cause them to dry prematurely.