Loving your posh new name "Impereale"...
FeelingMisled You slave-driving him is the worst possible thing for your relationship - who can respect someone they have to slave-drive? Who can love someone who slave-drives them? So that has to stop. You say you're fed up with mothering him - so stop it. Much as I agree it's his fault that he needs mothering, I also think, in the gentlest possible way, you have a choice about how you react to him and you are choosing wrongly. Stop being concerned about his future like this - he isn't! Rid yourself right now of the temptation to be a martyr to other people's needs; your life will be better for it, trust me.
But I don't think you need to break up with him necessarily, unless you want to. It depends what's important to you. If he has a ten inch solid gold dick, or really loves the same nineteenth-century French poetry you do, or whatever, he can still be a boyfriend, he just can't be a partner. If your priority in life at this point is to forge a successful future with a partner, he ain't it.
You're about to get your own place, great, you'll move onwards and upwards. As you say, don't let him move in rent-free. He has to understand that there are consequences to him not taking his place in the adult world. That might make him get off his arse. Or he might carry on drifting in the doldrums and you'll finally get fed up and the dick/poetry will no longer be enough and you'll move on to more grown up men.
Just one thing I have to flag up - this sounds like me after I graduated, and I wasn't lazy, I was very, very depressed and underconfident and I hid it very, very well (and I also got extremely defensive if people tackled me about it). I'm throwing this in just in case it makes a light bulb go on for you. TBH he probably is just lazy. Even if he is depressed, I don't think it changes my advice.