First, there will be no rain-shortened games. If you've played 6 innings, and it starts to rain, the game is suspended and will pick up at a future date where the game was suspended. We may see a lot of partial double-headers where the teams play the last 2 innings of yesterday's rain-shortened game, then play another full game.
Second, there will be no shared equipment. Things like rosin bags and donut weights will be taken to and from the field by individual players. When a pitcher goes out the the mound, they'll carry their own rosin bag. When the half inning is over, they'll take their personal bag back to the dugout.
Finally, there will be no carrying of equipment by a player/coach. If a player ends an inning stranded on second, nobody is going to bring out their glove and hat to them and take their batting helmet back to the dugout. The player will have to go back to the dugout themself and carry the batting equipement with him and retrieve the fielding equipment. I'm not sure how this is going to work for players who wear 10 pounds of armor in the batter's box, then take it off and hand it to the first base coach when they get on base.