Cuteness overload, I agree.
I don't think Bubbles was watching Faye sleep or anything -- in the first panel it looks like she was on her back when Faye started talking in her sleep (couldn't have been on her left side because of the charging cable). She then pulls her charging cable out to face Faye and starts cuddling her while responding to the "bear king" dream...
Dreaming and sleep talk is just one of the many bio-brain quirks that AIs (and humans, for that matter) find charming, fascinating, and inexplicable.
I love the flexibility AIs have regarding rest and sleep (and charging). Back when Momo got her new chassis, she told Marigold that she didn't need to sleep, so she could work at night and pay Marigold back for her chassis (and Marigold told her it was a gift, not a loan). And May seems to be quite flexible about the shifts she works.
So AIs may not need sleep, or at least they have the conscious choice to move, compress, or defer their periods of rest without the resulting confusion and grogginess that afflicts us meatsacks.
Bubbles has been woken up a few times and seems to instantly come to full awareness, which makes sense. If I were to redesign human brains, I'd certainly install the ability to consciously control rest and awareness.
But sleeping and resting are essential parts of the human or sentient experience (not to mention staying in one place for a while is necessary to recharge). Maybe they defrag or run repair routines while in sleep mode.