These were a recent purchase, so they had a very strong smell of "paint" out of the box. First thing I did was submerge them in water. It's obviously non glazed because you can see the air bubbles coming out from within the clay. I'm wondering if it's safe to drink hot beverages from this type of material or even drink from it at all.
Potter here, weighing in at Stephie's request.
What we see on video is sufficient to determine that the mugs are not vitrified ceramics. Vitrified means that the clay has been fired to a temperature where the silica in it turns to glass, making it waterproof. Generally speaking, you want most food-related pottery to be vitrified. Certainly those mugs are not safe to use in the microwave or the dishwasher.
Non-vitrified ceramics do have food uses, though. For example, a lot of traditional baking dishes are non-vitrified, because their underfired nature actually helps deter cracking. And in India, it's common to use very underfired ceramics in place of disposable cups; you just need to drink from them quickly, before they start to seep.
All that aside, there is no good circumstance under which any ceramic item used for food should "smell of paint". Any glaze on the pottery would have been through at least a 900C firing, and as such will have no smell at all. That points to some kind of paint or sealant being used on the mugs, and if that substance is not documented you have to assume that it might contain toxic materials. Also, if the vendor did not mention using sealant or paint, you have to ask what else they might not have mentioned, such as lead or cadmium in the clay itself.
Your video shows that the clay is not waterproof. This means liquid will be absorbed into the clay, which then can harbor mold and bacteria and contaminate food at a later time. This is why unglazed pottery is generally considered not food safe (with some exceptions for types of pottery that develop a closed, glass-like surface like porcelain). The temperature of the liquid will only influence the speed with which liquid gets absorbed, not the general principle.
That said, there are types of unglazed clay pots used for cooking, but they are typically heated so hot and for so long that food safety is ok (-ish, you still want to clean them meticulously and keep them dry to prevent mold), unlike drinking vessels, and the clay itself must be non-toxic, of course.
In short - if there are bubbles, there’s a potential problem with food safety.
Personally, I’d probably use the mugs as decorative objects for non-food items, just to be on the safe side. And if they are really unglazed, I’d also not use them as vases, because there will be moisture on all sides, including the bottom (speaking from experience, when I was younger and naïve).