The garden-side neighbor wouldn't matter to me. I'm more interested in border garages or because on the side you often only maintain the 3m distance, what heights the side neighbors have. Are there already any facts to orient oneself by?
And of course, I would clarify that with the approval authority, the height indication in the submission plan is to be taken seriously - however, I would see 10 cm more or less height as just a correction, like shifting a window (naturally while observing the maximum heights, which probably won't be touched anyway).