It depends entirely on how the votes are structured, the issue at hand and what the articles of the company say about the particular type of issue.

On the board that I was on we had normal matters which required a simple majority except that some members had 2 votes and some got 1. Then there were "Supermajority matters" which had a different threshold and "special supermajority matters" which had a third threshold.

Generally unless the articles say otherwise I think a quorum means a majority of votes are present[1], so 4 out of 6 would count if the articles didn't say you needed say 5 out of 6 for some reason.

It's a little different if some people have to recuse themselves for an issue. So say the issue is "Should we fire CEO Sam Altman", the people trying to fire Sam would likely try to say he should recuse himself and therefore wouldn't get a vote so his vote wouldn't also count in deciding whether or not there's a quorum. That's obviously all BS but it is the sort of tactic someone might pull. It wouldn't make any difference if the vote was a simple majority matter and they already had a majority without him though.

[1] There are often other requirements to make the meeting valid though eg notice requirements so you can't just pull a fast one with your buddies, hold the meeting without telling some of the members and then claim it was quorate so everyone else just have to suck it up. This would depend on the articles of the company and the not for profit though.

That's a supermajority in principle, but the board originally had 9 members and this is clearly a controversial decision and at least one board member is conflicted, and another has already expressed his regret about his role in the decision(s).

So the support was very thin and this being a controversial decision the board should have sought counsel on whether or not their purported reasons had enough weight to support a hasty decision. There is no 'undo' button on this and board member liability is a thing. The probably realize all that which is the reason for the radio silence, they're just waiting for the other shoe to drop (impending lawsuit) after which they can play the 'no comment because legal proceedings' game. This may well get very messy or, alternatively it can result in all parties affected settling with the board and the board riding off into the sunset to wreak havoc somewhere else (assuming anybody will still have them, they're damaged goods).

It depends on the corporate bylaws, but the most common quorum requirement is a simple majority of the board members. So 4 is not atypical for quorum on a 6 person board.