I do not see the garage position as the main problem, but rather the entrance in the north. For this property, I would only place it on the east side. For that, you have to start over with the floor plan.
I find the 3m distance of the garage neither fish nor fowl. Either 5m distance so that visitors can park in front of the garage, or the garage right at the corner. My favorite is the 5m.
What work is supposed to be done at the workbench in the garage? With an interior length of about 6.4m and a car of 4.7m (e.g., Audi A4 Avant) + some tolerance between car and gate, not much space is left.