I feel like I can't just stop hanging out with the other guy because he is mentally in a delicate place and it won't be a good idea for me to ghost.

Oh come off of it. First of all, of course you can, you do not want to stop spending time with this other person. You want to keep pushing your boundaries, you want something to happen with this other guy, and naturally you will do what you need to do to keep things going with him. This includes minimising the blame of your own actions and choices by deflecting on to a depressed person as to why you need to hang around with him. Any why would you need to ghost him? The steps here are about as simple as they come.

Step 1: Hello boyfriend, I have been having an emotional affair with XYZ. I started getting feelings for him after spending so much time hanging around with him. I recognised the feelings as just a novelty attraction and realised this was not what I wanted so I am breaking contact. Step 2: Hello other guy, it is best we do not hang out any more because it is damaging my relationship. I'm glad I have been able to help you out as a friend, but things have changed. Here is the number for some therapists I've found. It turns out they're infinitely more qualified than an infatuated young girl to actually give you real help. I know right...there are actually people who studied for 4 or more years to become doctors to treat this sort of stuff, I had no idea either! Best of luck in the future.

But I just can't help but feel like for some reason I am suppose to be with the other guy.

Pretty basic infatuation stuff here. You're in the fog before clarity, all new relationships start off this way. This is so generic that its about as interesting as watching grass grow.