@Habiddiaz
I faced the same issue last month. Refer to my post : Data&API (Integrations)- Getting failed to fetch Supabase projects error
I have submitted a bug report for this.
Workaround : First use the supabase plugin in the interface tab (not from the Data&API) to connect. Second Don’t use supabase branches, instead duplicate your supabase project and use the second project for editor/staging and use the first project for production.
Obviously any backend changes on supabase won’t ‘merge’ or sync on their own and will have to be manually replicated from your duplicate project to the original one.