I couldn't find starting pitcher information, but last year Cleveland faced left handed pitching for over 31% of their plate appearances. The Yankees, OTOH (literally I guess) faced left handed pitching at a 19.6% clip. There are limits to the gamesmanship, of course. I'd definitely rather face Tommy Milone or Dallas Keuchel than any of the starters that the Twins used in 2023, but clubs will do what they can to maximize an advantage.
After some further research, it appears Cleveland faced 59 left handed starters (36.4%) last year. Maybe 40% is out of range, but 35% might be about what a heavily left handed hitting roster might face.