Taalib, see thisI am not sure about what the Saudi majlis and Omani sabla traditions are, but their linguistic origins make clear their shared meaning with the Kuwaiti diwaaniyah.
I know that in Kuwait, the diwaaniyah is a men-only weekly or biweekly gathering within a designated area of a family home, where relatives catch up and dinner is often served. It is a wonderful thing to experience as a foreign guest. Which brings me to the point--much formal (that is, MSA) Arabic usage of the Persian "divan" denotes something very formal and usually political: an administrative council, a secretarial office, etc. The Kuwaiti diwaaniyah can be sometimes political but is more of a social gathering and has cultural meaning far outside its linguistic context.
Can the same be said for the Saudi and Omani context? I've never been to either country.