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This is what real Tang dynasty "pots" (壺) look like:
Sources: Left, National Palace Museum | Right, Christies's
As you can see, a hu (壺) is more similar to a modern vase than pot. The item in the first image you found isn't anything historical or even an imitation of one. I suppose it is stylistically somewhat similar to this silverware item, which is classified as an unusual zun (樽):
Note that bronze vessels, as mentioned in the question, went out of fashion after the Han dynasty as ceramics began to displace bronzeware. Designs likewise often evolved over time, so it's not necessarily possible to draw a direct line from Zhou classifications to Tang usage almost 1000 years later.
However, items called as hu (壺) did exist in the Pre-Qin era (often, inscribed on the item itself). They look not altogether dissimilar from their Tang descendants:
Sources: Left, National Palace Museum | Right, Sotheby's
With bronzeware, the zun (尊), jia (斝), and jue (爵) all refer to specific types of vessels with distinct functions. The zun (尊) is for holding the wine, jia (斝) is for warming it, and jue (爵) is for the actual drinking.
A hu (壺) serves a similar function with the zun (尊), but differs in having a smaller opening as the images above demonstrate. A zun (尊) is typically an impressive, towering work that looks like:
Source: National Palace Museum Facebook
The classical bronze zun (尊) was impractical and rather more ceremonial in nature, causing it to die out soon after the Zhou dynasty. At the time of the Tang dynasty, wine was poured into a the phonetically identical zun (樽) before being scooped out for drinking: