Are you finished university? If not, you could look at listings for shared housing.
OP, I know that it feels like you don’t have options, but you really do. After marriage, children, buying property together , your options become more complicated, and the stakes get higher.
There is always a compromise in situations like these. Which compromise are you prepared to accept? Leaving your cats or being in a dead end relationship?
The thing is, people in situations like yours often stay because things aren’t horrible, and there are still warm feeling for your partner. But then, loneliness happens. Or one of you meets someone who you have strong sexual feelings for, and things can get ugly. Then you can REALLY hurt each other without intending to.
Is there really no one who can have your cats for awhile? Or perhaps you can stay friendly enough with your partner that he will continue to house your cats? This is probably not the ideal option though.
I can appreciate it would be difficult to be separated from them but they will be ok. You potentially WON’T be if you stay in a relationship which isn’t functioning.