Calculation single-family house with upscale equipment

Yes, plus acquisition incidental costs, furniture, lamps, moving, etc. that cannot be financed. However, your own contributions can (realistically!) be set off against this, provided they are not already included in the 315K€. Assuming 80% is the limit. You need to inquire about that.

Sorry, I didn't have the garage on my radar. I would say your budget is not enough then. A solid garage of that size easily costs 20k.