The neighboring garage is not shown in your elevation plan - but where I locate it, the natural ground is 6 cm below your finished floor. Therefore, for your house, I do not see the need for backfilling afterwards - a little redistribution seems sufficient to me. However, for your neighbor's request, it only matters whether and how far you have excavated - which you have not, if I understood correctly. mentioned that at another place - unknown to me - your brother contributed further details for clarification, which I obviously cannot assess here. From my point of view, the neighbor simply failed to consider his unauthorized built height when founding his garage. "Small sins are immediately punished by the kindly God," was a saying in my childhood about this.