I'm aware that ancient Romans had spectator sports open to commoners - gladiator tournaments, fighting animals, ship battles, contests similar to the Olympics, etc. Romans had their favorite athletes and would go to see those particular athletes play / fight. They had organized athletic groups and established, purpose-built venues that existed primarily to entertain the crowd. Today we obviously see the same dynamic with sports teams, stadiums, etc. But what about in the middle?
How did that work with medieval games and tournaments? Were commoners invited to things like jousting tournaments? Were there sporting venues that existed primarily for crowd entertainment? What sports did they play? If not sports, did they do anything else (circuses?) to entertain crowds?
Romans had their favorite athletes and would go to see those particular athletes play / fight
They still did this in the Middle Ages. Remember, the Byzantine Empire was the Roman Empire in the Medieval period. One of the great spectacles in Constantinople was the massive Hippodrome, where various racing and ceremonial events (gladiatorial combat had fallen out of style by this point) were held, really until the sack of the city in AD 1204. It was over 1,000 feet long and 400 feet wide, and could accommodate approximately 100,000 spectators. Constantine VII's De Ceremoniis elaborates in excruciating detail the various rituals that were supposed to be performed by the Emperors when entering the Hippodrome for the start of the Games, and that was written in the mid 900s AD. There are also mentions of the races in later works of Psellos, Attaleiates, Anna Komnene, Kinnamos, and Choniates, telling us that these races remained popular in Byzantium at least until the 13th Century.