I dont even know what that means.
It is a running gag generated over the past few pages of this very thread. A conversation we have all been taking part in, btw, so you aren't being excluded.
No there aren't and the actual definition of Mary-Sue doesn't support your claims.
https://www.dictionary.com/e/fictional-characters/mary-sue/
Mary-Sue's apart from being an avatar of the writer also have zero flaws. Picard has flaws. Picard left starfleet in protest and then went and hid in his chateau and spent 14 years ignoring the people he had promised to save. That was a pretty hypocritical move on Picard's part, how dare he criticise Starfleet, when he did absolutely fuck all.
Remember when "Mary Sue wasn't derogatory? When it was an in joke between trekkies who read fan fiction and was used affectionately?
Oh, for context:
https://www.studiobinder.com/blog/what-does-an-executive-producer-do/
An executive producer (EP) is the head producer who supervises other producers in the creation of a film, television show, web series, commercial, or theater performance. They may work independently or on behalf of the studio, financiers or the distributors.
They will ensure the film is completed on time, within budget, and to agreed artistic and technical standards.
In television, an Executive Producer may also be the Creator / Writer of the series.
Bottom line: An executive producer is usually a financier of the project. Typically, this person may assemble the core team, but will not physically produce the project.