Thank you for all the answers.
Buying a private property and selling it if necessary, if it works with the municipality, is not possible due to the financial situation and because the municipality does not sell properties to people who already own one.
With a job change, the private property becomes less interesting and the commute would presumably increase by 5-10 minutes.
Unfortunately, home office is out of the question for me, I work as a maintenance technician. For my wife, it will probably also be a long time before that is an option.
Shopping facilities are not on the way from the private property.
On Saturday we have a viewing appointment with the seller, but I don't quite know what I will say there yet. Some friends and family live closer to the private property, but that would mean about €200 additional costs per month that would grow with inflation for the commute. A friend even lives on the same street, but both have home office and are financially better off. Houses are no longer cheap and we are already trying to build as cheaply as possible, so the additional €200 really hurts. Plus the difference in commute time. After all, about 30 minutes per day are lost additionally. In general, I still find up to 30 minutes commute time just bearable if you can't get anything else.