Sometimes things change and you have to rehome pets - it does not feel good, but it is the responsible thing to do. There is a responsible way to do it, and an irresponsible one. Nowhere has OP indicated an irresponsible approach.
OP, I did wonder if this perspective would change for you if you got more help, found alternatives for stimulation for the cat and were a few months down the line. But if not, there is nothing wrong with your decision.
I am going to take up this point from @TatteredAndTorn though.
(And No longer being friends with someone because they rehomed a pet is ludicrous)
Its not the actual decision to rehome, always, it is the behaviour around it. For example, looking at putting a healthy animal down because you cant be bothered to work with agencies to rehome them is truly disgusting. I fell out with a friend because of this. She was desperate to move with with her (obviously reluctant) boyfriend and as a last ditch attempt, he told her she could only bring one of her two cats with her. She called his bluff (yeah, it did not last, big surprise). Having doted on her cats for 10 years, she showed up with the boy at mine, crying and saying if I did not take him she would have to have him put down. I said I would do two weeks while she made arrangements because I had 3 cats of my own at that time, and did not feel I could take on another permanently. Guess what? She did not do shit, just waited it out, ignored my reminders that it was temporary, and when I told her 2 weeks were up, sent me a list of what I could do to rehome him. I did not know at the time she had made zero attempts to rehome the cat. What really finished the friendship was how she was willing to treat me. I had no respect for her after that, and it was clear she had none for me. I found the cat a nice home and made some better friends.