I am a solo traveler on occasion, but I just meet people around the ship rather than attend gatherings. My guess is at the first meeting, the solos themselves decide on possible future meetings.
There are no solo tables in the MDRs that I am aware of. You can agree to share, especially at breakfast and lunch. I do find that sharing is less of a thing post-COVID, although if you'd like to share, you can. (Immediately after the restart, there was no sharing.)