I have been observing this in my bunnies for some time now. I actually think it’s a form of relaying contentment and I also think it is some form of communication. I first discovered this when I would give Jack kisses on his head — and he’d do the “purr” noise back. Vivian does this too. I just figured he was purring, but then later I watched Jack do this while hanging out by himself with Vivian a few feet away. He would do the little soft mouth chomp/slight purr and then she would do the same thing. They’d go back and forth a couple of times doing this. So I started to make quiet little non squeaky “kissy” noises (trying to sound more similar to the noise they were making), while I was several feet away, and low and behold, Jack would then make the little purr sound back.
I’ve tried to figure out what it is and I thought maybe at first it was a request to come over and groom as that would sometimes happen between Viv and Jack. But as time went on, I got the sense it was more like a checking in with each other and with me….as if to say…”You there? All is fine here. Don’t sense any danger, just chillin, what about you?” and Viv would respond…”Yep, quiet over here too, just chillin”
Of course that’s not what they are really thinking — I’m just adding human interpretation, but it just felt like they were telling each other…”it’s okay to relax, all feels fine here at the moment”