Officially the only events in 5e's storyline with the Thay have involved some necromantic debacles...
Two sundering related adventures happened between 4e's official end of publication and the release of the PHB. Ghosts of Dragonspear Castle kicked off the Sundering event which is a reboot of the Forgotten Realms lore and the Red Wizards were the antagonists in the Dead in Thay adventure which operated on the Playtest rules and not the official rules released later. In it, there were a fair bit of magic items, but everything hinged around a location of immense power, the doom vault which also served as sort of a magical creature menagerie and no wider look at teh Thay was given. As a result of the events of this adventure the Thay have essentially been displaced from their lands an while they still have enclaves around the world, their powerbase has been severely diminished.
5e's reduced magic item economy makes magic items out of the reach of individuals (usually), but they remain in the reach of organizations
As you state (and as I have interpreted from everything WOTC has said so far) you can't just buy and sell magic items in a shop, but they are still usable, desirable items. Naturally the five factions (and antagonistic NPC factions like the Cult of the Dragon) want these powerful objects to help further their goals. PCs may be rewarded or loaned these items when they rise in the ranks of the factions and/or be able to try to sell these to factions.
Treat the Red Wizards as a necessary evil that the factions allow to a degree because they desire the power and utility of the objects they can provide
Thayvian society is basically an oppressive mageocracy and the Thayvians themselves should be looking to trade rare magic items for large sums of money, rare luxuries, treaties, land, and most of all influence. A small group of adventurers is probably far below their notice as possible customers unless they can generate interest with something to offer Thay that can rival what the Lords Alliance or Zhentarim might.