What are all the chess.com offically recognized leauges on here for team and vote matches ?
You can find some leagues in the Leagues listing group.
Which are the more notable ones ?
There are several notable ones. I'll try to make a short summary.
Vote Chess leagues:
I think the most notable is those in the Vote Chess League group. They have for example Open Swiss tournaments that are very popular. Then comes Chess.com Super Cup (CSC) which have a knockout tournament where a new tournament start at the beginning of each year. Then there is Speed Vote Chess League Headquarters for speed vote chess (10 min/move). Lastly I also want to mention World Cup of Chess Openings where a team chose an opening and will play 2 games each round. One with their opening and one against their opponents opening. I think there is no sign for a new World Cup of Chess Openings tournament to start, but the other 3 I mentioned currently have a tournament which is open for registration. Vote Chess League Headquarters will also host a chess960 tournament in the near future.
Team match leagues:
I think the biggest is definetly World League which is for national teams. Then I'm not sure, but I think the notable ones afterwards are TM League Headquarter for the strongest teams and Chess.com TM championchip for those not participating in the World League or chess.com TM League. For small teams the Chess Olympiad Quad League could be interesting where there are only 4 players/team in each match. I don't know if any team match league is open for registration or when the next will start. If your interested I recommend joining the group managing the tournament and ask in the notes.
Lastly I want to add that there might be some good leagues in the Leagues listing group that I forgot to mention or don't know much about.
Thanks very helpful.