Split because I'm seeing potential for an alternate direction of discussion here. (We tend to do that, and yes I'm amused by the multiple system that causes a need for many splits.)
Who-all here has tentacles? What are they good for?
My people generally keep energy tentacles out as a matter of habit; we're used to touching each other energetically on a constant basis. (Val has surmised that being in a multiple system is probably the most comfortable way for us to be in a species that doesn't have this constant contact. She's probably right.) This is a big part of why we tend to be xenophobic. Anyone outside the tentacle group hug doesn't seem like a target for empathy because, in our native form, we're used to "empathy" being intravenously fed to us by our tentacles. We still hurt each other, sure, but there's usually a limit to that and the more group-huggy we get with a person, the more likely we are to fall into groupthink.
We think it's also why we as a system have the shared energetic body anatomy that we do; it's been described as being like a giant robot in which we each have our own little bubbles of self. The need to touch in that way seems to mesh logically with the idea that we collectively put together this shield/shell to contain us all.
As for physical tentacles, Rhun was more shapeshifter-y than the rest of us seem to have been - something our people believed was a result of either outbreeding with more polymorphic races or traces of older, wilder blood. The latter has to do with an origin story that's pretty high on the woo meter, and we recognize that, but Rhun remembers having lived during that time, so we tentatively embrace the woo.
Aside from flexing 'em for the sake of flexing 'em, the way that he wraps them around people he cares about - and is therefore protective of - seems to just be a showier version of the displays we'd make in order to show where our connections lay, who we were allied with. But aside from that, Twilight got where I was going with my earlier ponderings. Kung fu Cthulhu's tentacle grip from all directions seems like a great move for a stealth fighter, which Rhun was for part of the life that he remembers in most detail, and which Shainin preferred while she was shifted to crab spider - she didn't have the tentacles, so she had to become something with extra limbs to do it. (And, as I'm now remembering, she also does the thing with enveloping others...when she thinks it's safe; our sweetie is afraid of spiders...)
"All knowledge is worth having." -Phedre no Delaunay
"Everything has a price." -Jaenelle Angelline
"I think if you try, that's being your best." -Echo