I know that Tenochtitlan's government had a great deal of bureaucratic complexity, so I imagine that there was a variety of civil officials involved in this, and indeed, The wiikipedia page lists titles known as Petlacalcatl, Huecalpixque and Calpixque as officials involved with this process. Who were they? Were any others involved? For that matter, were the Pochteca purely private trading guilds, or were there state operated Pochteca?
Also, I say "Aztec empire" here rather then just Mexica or Tenochtitlan, because traditionally it is said that tribute was also sent to Tlacopan and Texcoco, so I am also asking about how it worked for them as well; and this post notes that it Texcoco and Tlacopan may not even have been uniquely owed tribute and rather that tribute was redistributed to a variety of other cities in general.
Great question! Increasingly research has shown that the Aztec Empire's structure functioned in order to both amass tribute revenue and to spur trade and market exchanges with and outside the empire itself.
Structurally, the Aztec empire had a lighter bureaucracy than other empires, for example the Inca had a much more extensive civil service. Part of this is due to the fact that the Azteca did not impose direct governance on all conquered or incorporated communities. Instead, tribute and gift exchange systems established hierarchies within the empire that connected communities to larger regional centers and then to Tenochtitlan.
There were two types of relationships gift-givers and tribute payers. Communities incorporated willingly typically became gift-givers while those who were conquered became tribute payers. Gift-givers had a privileged position and were more likely to see reciprocal gifts from the imperial elite. Tribute payers had less leverage and less status.
In general both gift-givers and tribute payers were required to provide some goods that could not be produced locally. For example, if a community typically produced fine cotton cloth they would have to provide some of that but they might be required to pay quetzal feathers too. To acquire those feathers the community would need to trade for them.
This system fostered the growth of commercial networks as elite forged new relationships in order to acquire tribute goods they increase non tribute-based trade as well. This had the tendency of increasing existing patterns of trade in which local elites purposefully entered into trading relationships in order to acquire sumptuary goods and other rare commodities in order to emphasize their station and forge ties to other elites.
I'll add some citations later