The companions are never shown to be with anyone else, so open relationships are really just "open" on your side.
Sorry but you are just using confusing language. The companions are never shown anyone else you say but are they exclusive to mc or you just don't show that in the game but they still fuck with others-customers at the background? If they are exclsuive to mc, in the game they should tell you that. Like 'I'll be only with you, I won't see anyone or any customers'. When you said 'they never shown with anyone' it sounds like 'they are fucking with others but you don't see or hear about it'. Just say they are exclusive to mc and they will tell you that in the game if that's the situation. Because if they still be with others but not shown or get mentioned in that that 'open relationship' then it's still not Harem. They would still fuck others in the behind the scenes so it doesn't even matter if you don't even mention it in the game or just directly show them having sex with customers. It literally has no difference. The game should state that they don't work as courtesan anymore and only have sex with you when choose to have a relationship with them. If otherwise open relationship route isn't harem at all.
Exclusive/harem route would sound less confusing. The exclusive route is simple where mc can only be with 1 girl, that girl stop being a courtesan only have sex with mc and they basically become a romantic couple. In the game they both should state that they are exclusive ot each other. On the HAREM route mc can be in a relationship with multiple girls and the girls she is in a relationship tells mc that they won't fuck with anyone or any customers, they stop being active courtesans so they only sex with mc only and they are fine with other girls who are in a relationship with mc. That's is harem route. Your 'open relationship' route and how you describe it is extremely suspicious that kinda implies that girls are still having sex with their customers but you just don't see it or get mentioned in the game. For the last time you cannot call it 'harem' if girls fucking with others, whether you show it in the game or behind the scenes doesn't matter at all. When they will be in a relationship with mc, they should tell mc that they are exclusive to mc and mc is the only one who can have sex with them so they should stop working as a courtesan and so they can stop having sex with customers. If they don't do that then players can assume they still work as a courtesan but you just don't watch or hear or get mentioned them having sex. It's all in the background.
With how you describe it, I sadly think open relationship is not HAREM at all, you just don't watch them or hear them or get mentioned in the game having sex with customers tbh. Please correct me if I'm wrong and girls are completely exclusive to mc when they go in a relationship with him and they tell you that in the game. If open relationship route is not harem as I suspected, I hope at least on closed/exclusive relationship route, partners states in the game to each other that they only have sex with each other and the girll who you in an exclusive relationship with stop working as a courtesan and in the game she tell you that. Basically become a loving monogamous couple
