Indeed I agree with you, the garage should remain on the half farthest to the living room, dining room for functional reasons: creating links between the new spaces (office and bedroom) and existing ones, as well as avoiding the garage to be a central space in the new proposed area.
However, there must be a hallway so that the garage can still be accesed through the house. From this hall there are links to the bathroom, the bedroom, the existing spaces of the house. It can become a mudroom, if you need one.
The office is placed to the exterior wall. It can be accesed by passing through the bedroom or directly from the living room (I proposed a small change in the living: adding a plywood behind the couch and a simple door in the same color as the wall).
Because the new walls could not respect the roof's divisions, I tried to make the best of it by using its beams to hang the lights in the bedroom (circular pedants which go with the french doors to create a certain atmosphere). Also the plywood in this room makes the bed the central piece of the room, emphasising the wall lights. It also offers a nicer view from the office.
In the office the desk and plywood are symmetrical to the shelves on the opposite wall as to create a sense of order, as well as a functional space in which the doors can open freely.
I hope you will like it!