Maxi's extension was 1 year with an option for 2023. It does not says whose option, but I think in MLS it is a club option unless specified usually.
New York City Football Club Midfielder Maxi Moralez Signs New Contract | New York City FC
NEW YORK, N.Y., January 1, 2022 – Off the heels of winning its first-ever MLS Cup championship, New York City Football Club (NYCFC) today announced that midfielder Maximiliano ‘Maxi’ Moralez has signed a new contract with the Club through the 2022 season with an option for 2023. The Argentine...www.nycfc.com
I believe all options in MLS are team options, they don't do player options.