You are quite clear on what you want - a relationship where you and the loved one (or more than one perhaps) would live together, spend most of your free time together, and develop mutual interests. This seems to be your preferred style of developing deep connection and intimacy.
There is absolutely nothing wrong with this. There is nothing wrong with you for wanting this style of relationship.
But you can't have this with M, your girlfriend. She is also very clear that she does not want this style of relationship. And, there is nothing wrong with that either. You and she are fundamentally incompatible, despite your mutual love and best efforts.
It's time to break up, move on, and let each other find others who fit better. I'm so sorry but this is a deal breaker. One should never make oneself 'less' for another person, even out of love.