You're basically right.
picta from pingo has a range of meanings including "adorned," "decorated," "dyed," "colored," "painted."
purpura is a noun meaning (among other things) purple cloth
We might translate "veste" using a plural.
"the couches are strewn with colored vestments and Tyrian purple cloth"
In antiquity, formal dinners were eaten reclining on couches, not sitting in chairs.
Tyrian, or Phoenician, purple dye, which was made by cooking certain kinds of shellfish found in the Mediterranean on the coast of Phoenicia, was a luxury item. "Tyrian purple" reminds us of Dido's (and Carthage's) Phoenician origins.