A Cyclops can actually carry (and protect from crushing depth) either a Seamoth or Prawn Suit, but not both at once. The sub will also charge any docked vehicle from its own power reserve. Problem is, not only is recharging a Cyclops kinda a pain, but the thing is pretty big and bulky, and thus hard to maneuver in tight places.
Funnily enough, there were a couple tricks in earlier versions of the game relating to the Cyclops. In very early versions, you could put stuff on the exterior of the hull with the Habitat Builder, so people quickly figured out that Solar Panels would recharge the sub as it goes, both counteracting the generally poor power economy of the Cyclops and allowing for on the fly recharging. However, the interactions of things in this trick was kinda wonky, so the devs patched it out.
In exchange, they created the Cyclops Engine Efficiency Module to compensate for it... which had its own trick early on. In the first few versions with it, the Cyclops Engine Efficiency Module didn't just affect the power consumption of the engine, it also affected all installed modules and anything you built in the Cyclops (that used power) with the Habitat Builder... so people would build Power Cell Chargers in the Cyclops, and fully charge Power Cells (200 power) at the "cost" of something like 50 or 100 power, then cycle out drained Cells for the newly charged Cells, thus giving you effectively infinite power in the Cyclops. The devs, unfortunately, patched that one out fairly quickly when they found out about it, and now the Cyclops Engine Efficiency Module only affects the power draw of the engines when used for propulsion.