They play this year. I was unsure if they kept track of that sort of thing, but I did find reference to the 2020 season, where the Dodgers were favored in all 78 games (including playoffs). That was of course a shortened season. I wonder if there has ever been a complete regular season where a team was favored in every game.

The rabbit hole led me to the fact that the 2023 49ers and 2021 Chiefs were the only NFL teams to ever be favored in 20 games.

With regards to the NBA, I found a 2-year stretch for the Bulls from 95-97 where they were favored in 185 straight games. It is by far the longest NBA streak since 1990.