If you want to go off-grid I would recommend in addition to PV+batteries also a passive house. In the long-term costs nothing beats good thermal insulation. https://en.wikipedia.org/wiki/Passive_house

The grid connection cost are so high because the high electric system costs, which are distributed to the market participants using grid connection cost: the transmission costs (upgrade costs of electric lines - digging earth is surprisingly costly, overhead power lines are cheaper but they are not for free, upgrade costs of transformers), costs of backup - Germany plans to build new gas power plants, which will have a very low utilization.