>It bothers her when I don’t look after things the way she looks after things, and it bothers me that she doesn’t live a chill life and want to bicker about these tiny things like not using a coaster, being too loud unintentionally, or not putting things back to where they belong.

Not sure what "being too loud unintentionally" has to do with the rest of this, Upset-Rooster-1655, but none of this seems unreasonable to me. (Use the coaster! Pick up after yourself and put things where they belong!)

>I want to care about her house like it’s mine, I don’t honestly know how to stop being clumsy, how to put the oven gloves in right particular positions, not to leave a bread crumb ever on the floor, or be always sophisticated basically.

What does "being clumsy" mean in this context? (Or "be always sophisticated", for that matter?) And how does it relate to sweeping the kitchen floor more often?

>I want to make this relationship work and go back to the fun mode.

Does "fun mode" mean no responsibility for the maintenance of your shared living space?

What do you think might help "make this relationship work" and is it showing respect for her house and belongings and cleaning up after yourself?