In spite of free energy, the process of making matter into what you want is so involved that Yamatai is still getting much of its materials from asteroids and mining because it's easier to alter existing matter. Because of this, Yamatai's energy-to-matter technology is not fully harnessed and is used to make stuff like massive diamonds, graphene nanotubes, rods of pure titanium, and other elemental products that can be used by industry, as well as compounds like Durandium and other materials like super plastics, advanced ceramics, and low-friction personal lubricants. For a major example of free materials in Yamatai, the value of gold is largely symbolic because they can basically print it out of aetheric plasma. This is not a unique example but it's not the norm either. The real benefits of energy-to-matter come into play when they're making very rare substances that are not easily found or mined (think of the rare Earth metals in China that manufacturers need to make iPhones).
Overall, energy to matter conversion doesn't really have much effect on the overall economy outside of the industrial sector, and it is directed primarily at making stuff for Ketsurui Zaibatsu product lines and (surprise, surprise) the Star Army of Yamatai.
Valuable items are technology, real food (not algae synth stuff), and--to some extent--wood. Services are labor are valuable and make up a lot of the jobs.
Cheap stuff in Yamatai: Because Yamatai is big and has tons of frontier worlds, land is really cheap right now in Yamatai. Starships and vehicles are surprisingly cheap in Yamatai.
I wish I could say more but it's a really broad question (although really good to ask about the setting).
It makes me wonder if some independent trader character will start a lucrative business selling Yamataian gold to the Hidden Sun Clan.