Data Pad: The slate, a once ubiquitous accessory before the advent of the fob terminal, the wearable, and the neural lace, and still quite common because it’s useful to pass data around (of course, smart paper does just as well for this, but…). Also, people kind of like working with their hands.
Also note that this is a way to share one or more documents on one person’s device among multiple people having a coffee together, not a stack of one-document-per-device data pads ending up in in-trays, this not being Star Trek:
TV writers of the 80s could foresee the tablet computer but couldn’t grasp the concept of email?
I guess you could gloss it by claiming that each tablet is connected to a different stovepiped and security isolated system. You know the Federation/Republic has to have an crazy complex bureaucracy.
Also, the Original Series foresaw the tablet in the 60s. Gene Roddenbery figured that it would be insane to take up all that ship volume in hard copy paperwork.
Star Trek was full-on paperless, but lazy writers then used all the paper tropes with tablets instead. So instead of stacks of paper in your inbox you had a stack of data pads there.