András has given you the good overall picture of what psocids eat, although there are variations and some groups are rather more specific in their dietary habits than others.
The species that become pests in homes and food storage (most Liposcelis spp) are primarily micro-mould feeders and require a high relative humidity for their food to survive. They themselves can survive lower relative humidity because they can extract moisture from the atmosphere provided it is not too dry. The damage they cause is not actually caused by their browsing directly, whether on grains, dried stored goods, or even books. What they do is eat the moulds that have already caused some superficial damage and as they do that they scrape off the surface layers of the substrate.
Some Liposcelis have even been found inhabiting (probably on an opportunistic temporary basis) the heads of people, especially when they go to bed with damp hair and probably with skin scales that have Malassezia yeasts on them. This is probably an extension of their normal nest inhabiting behaviour where they probably also ingest some of the skin scales. Historically this was probably the origin of the parasitism process that led to the diversificaiton into the Phthiraptera, where psocids living in nests found it easier and more convenient to move onto their hosts to feed there, changed diet initially to skin cells and subsequently to skin, feathers, and/or blood.
In some circumstances psocids of this type can become a major nuisance and controlling numbers can be really difficult as they are highly tolerant of insecticides and really only significant changes in relative humidity can cut the numbers. So for your desired aim of controlling mould and fungus in your terrarium I would proceed with extreme caution because you could end up with a worse problem than you have at the moment - but it would all depend upon the species you select. Better to start from a scarce looking species from the woods rather than a domestically derived one.
So good luck but if things look like they are getting out of control step in to deal with it quickly or else you may lose whatever else you are keeping there.