I'm not saying this isn't happening, the fact that the RSNs are (mostly?) owned by betting companies does not help.
But, anecdotally, my local (Angels) broadcasts don't talk about it at all. I listen to MLB Radio, and their day time shows barely touch on it (I'm pretty sure there's a odds making show on the radio, but not during prime time in the day).
MLB Network on TV, I do not see it in their main shows. MLB Central doesn't (I don't think, I'm honestly not a regular viewer) really touch on it. MLB Now doesn't, nor does MLB Tonight or Quick Pitch (their overnight highlight show).
There's ads, there's ads in the stadium (big BET MGM sign in Yankee stadium, for example).
So, anyway, on the periphery, it's certainly there, but the shows the MLB seems to put their brand on, I'm not seeing that much of it.
The closest I've see is on the Apple TV broadcasts where they might put up a "28% chance to get on base" in the corner for a batter. Interesting, perhaps, statistic, but I don't know that it necessarily encourages betting.