It seems that in Disgaea 7, you will be able to freely wander around the Netherworld and engage in minigames or buy exclusive items. As these are from leaks, we do not have videos or screenshots of these features yet. As well, until NIS reveals them in a trailer, there is no concrete information on when in the game you can access them. [Thanks, ryokutya2089!]
A new system called Netherworld Tourism will apparently be available in Disgaea 7. There will be special conversations that fill in blanks in the story, and you can participate in minigames. It seems like, through Netherworld Tourism, you can freely wander around the Netherworld in a way that you could not before. There will also be quests and battles exclusive to when you are touring the Netherworld.
One of the minigames that you can play is Netherworld Tsume Shogi. It is unclear if there will be a PvP feature for this minigame. There will also be a Hinomoto Martial Arts Tournament, in which you participate as one of eight teams. Finally, you will be able to purchase items that you cannot normally find in stores in the Netherworld shops. However, you have to first unlock the Netherworld Tourism function.
Disgaea 7 is in development and will come out on January 26, 2023 for the PS4, PS5, and Nintendo Switch.