From the Super Mario Wiki
The Entertainment Room is a location in Luigi's Mansion 3. It is found in the Mezzanine on the second floor of The Last Resort. It is south of the Restroom and east of the Ballroom. The purple Gem can be found here. The first Oozers in the game are encountered here.
When Luigi gets the fourth floor elevator button back from a mouse who ate it, it is eaten by another mouse who flees to the entertainment room. When he enters the room, he is attacked by Oozers with billiard balls, marking their first appearance in the game. After Luigi defeats them, he needs to use the Suction Shot on the middle locker to reveal the mouse, who then retreats to the restroom.
There is a billiards table in the middle of the room. There is an achievement Luigi can get called "Cleared billiards table in the 2F entertainment room". To do this, he needs to get every billiard ball into pockets in the table. If he does so, he gets the achievement as well as a bunch of coins. There are cabinets in the southeast corner. At the north end are three lockers. Luigi can pull them down with Suction Shots to reveal a hole in the wall holding money. There is a framed pig in the wall Luigi can spin with the Poltergust G-00. There is also a dart board nearby.
To get the purple gem, Luigi needs to pull down a sword from the east wall and shoot it at the dart board. It will pop open, revealing the gem.