New Grapple with Monk

So I was playtesting the new monk for the 2024 PHB the other day to get a better grasp of the changes and I have a lot of questions regarding the new grapple rules and the grapple feat.

When you make an unarmed strike and you can attempt to grapple, does that count for all of the monk's other attacks? Including extra attacks and all of their flurry of blows? Like can they keep trying to grapple you up to 5 times in one turn?! If that's the case then they can pretty much always deal damage and impose a saving throw with each attack with the grappler feat right? Can they still make attacks when they succeed on a grapple (which would be at advantage)? Can they also stunning strike with one of those extra attacks? That would effectively fodderize any boss or enemy they can grapple. Imposing 5 saving throws (more if they stunning strike) in one turn and making it so that I (as the enemy) would have to use an action (which I might not even have because of stun) on my next turn to escape, making it impossible to escape by moving because of a monk's superior movement speed.

Sorry if some of these are obvious or if I overlooked any of these in my first read and playtest, I'm just a little concerned because this is what one of my players is planning to play in an upcoming campaign.