I may have possibly overlooked which region you are building in while reading through the thread. Therefore, I will assume that you are staying in your current federal state, which is listed in your profile.
Hessen is comparable in price to Bavaria. We are currently building a house ourselves, about 140sqm with a basement. For the house and additional building costs (including a cistern and lifting system), we come to around 383k euros including upgrades for the bathroom and electrical work. Additionally, there are costs for garden design and a carport. We are doing a few things ourselves (installing underfloor heating, floors, painting) to keep the costs as low as possible, but at the same time we do not want to forgo a bit of comfort (basement at living room height with underfloor heating in one room, large children’s rooms, nice bathrooms with walk-in showers at floor level, preparation for split air conditioning, blinds on large floor-to-ceiling south-facing windows, well-designed network). But comfort is, of course, a matter of definition here.
It will be a solid brick house to KfW55 standard. If you want more, it naturally gets more expensive; if less, it can be cheaper. We are building with a construction company and pay the trades directly without going through a middleman (like a developer).
I therefore think that with the right construction company your budget is sufficient for a small house including a basement. It really depends on the level of comfort you want. Friends of ours, according to their own statement, come to a crazy 800k euros for a house (without land) with slanted rooms and a gallery. I find it awful, they love it. But to each their own.