So, Nick, for example, offers to hack a terminal. I activate him, turn to the terminal and press E. But all that's happening is me trying to hack it myself. Same with Cait and locks. Left mouse button only results in me shooting the thing.

The interesting thing is, as long as I don't point at an interactive object and press E, the companion moves there. But as soon as it's about any interactive object, the companion crosshair vanishes and turns into the usual dot.

There's some kind of weird, arbitrary distance you need to be at from the object for the right command to actually appear. Try moving away and towards the terminal until you find it.

Just be far enough away that you can aim at the lock or the terminal but not be close enough to do it yourself.