In the crew section you should be able to see the skill modifier for each trait, e.g. Depressed -10%. That's all the information the interface gives, there's nothing else hidden in a tooltip. All negative traits (including Depressed) get removed one level at a time when an explorer is in the hospital. There are also events that can remove the Depressed trait, but there aren't any tooltips that tell you that, it's something you're meant to discover through play.
Tooltips never give you information you can't get somewhere else. When a crew member gets injured or acquires a new trait, there's a tooltip saying what trait that was, but you can always see which traits they all have in the crew section. When the ship gets damaged there's a tooltip telling you which system was damaged, but you can always see which systems are damaged in the ship section. When you gain data there's a tooltip telling you how much data you got, but you can always see how much data you have in the status bar. So it should be possible to play without tooltips, just less convenient.
Maybe I could add an option that makes tooltipped text into links you can select to make the tooltip appear, rather than relying on mouse-over. Do you think that would work? It would mean the passage text would always be full of inline links, though, which I guess might make for a less smooth listening experience.
On another note: I uploaded a new version yesterday that adds music volume controls.