I think maybe the occasional T might do this, but the majority do not. I think most T's become T's because they care about people and want to help. It doesn't sound to me like your T is trying to manipulate you in this case, just from what you've written. It is his profession and he has to pay his bills, too. That doesn't mean he doesn't care about you very much. He is not allowed to have a relationship with you outside of therapy and to attach in the same way as a friendship, so yes, the relationship is confined to therapy sessions and he still deserves to be paid for his work. We all deserve to be paid for our work.
I have customers that I like very, very much and care about -- but I don't give them what I make for free or discounted if they are unable to pay for them. In my profession I'm able to be friends socially with my customers if I choose -- but in therapy that isn't allowed, so unfortunately yes the relationship can terminate if I were unable to pay my T any longer. That does not in any way mean that my T would care any less about me, but I understand that it is a paid service they provide. I understand that they too have bills and things they have to pay, and they absolutely deserve to be paid for their work.
I think your T asking if you could find a better job does not sound like it's about seeking money, but because he does care and would still like to help you if possible. He can't be your friend outside of therapy. But he does deserve to be paid, he is doing work. You deserve to be paid when you do your work. Him offering to see you every other week or once a month says to me he is trying to make it so that you can afford it better and still get some help. It really sounds like he's trying to help you, not hurt you.
That said, I know it feels really awful coming to the point where you might have to stop seeing him. It is a special type of relationship because you tell them so many sensitive things. It hurts to end a T relationship. It's totally ok to grieve this, it's normal!