Financing Home Purchase Assessment

I ask myself why there is so little equity available despite such high income?

It's in the first post… plus please read the words ;)

Unfortunately, it has an oil heating system from the 90s. Which data would be relevant here?

The problem with this situation is as follows: Oil is bad and may no longer be newly installed. The obvious replacement energy source is gas, but that has also fallen out of favor. Accordingly, you have to prepare for someone coming in a few years expecting you to install a heat pump when the heating system breaks down. A heat pump in an old building with radiators is not an inexpensive combination. Either you renovate the house (energy-wise, underfloor heating -> new floors everywhere) or you try to install a gas heating system before the deadline and postpone the problem. What about the water and electrical wiring? Are those already new?

With the oil heating system: by 2026 a new oil heater would have to be purchased, then the heater is new and has protection of existing rights and there will be peace for the next 30 years. However, if a gas connection is available or possible, I would have a gas heater installed.

It's not that simple. In BW, there is already the Erneuerbare Wärme Gesetz which obliges one to operate a part of the heating with "renewable" energy or to take other compensatory measures. Simply installing a new burner next year is not possible; presumably, the most cost-effective compensatory measure would be a photovoltaic system on the roof. However, this would need to be examined in detail.

Well, you can simply install a gas burner that can technically be combined with solar thermal energy.
It doesn’t have to go on the roof immediately as far as I’m informed, it just has to be possible.
An oil heating system from the 90s doesn’t have to be replaced right away. The boiler is definitely already low-temperature or maybe even condensing.
Only constant temperature boilers have to be replaced if they are older than 30 years.

Regarding financing: it’s feasible at first since there is sufficient income. Nevertheless, you are already tying a huge burden to your leg.
Aren’t you also underestimating the renovation/refurbishment costs? Just a new bathroom and kitchen, those 50k are gone quickly. If then the electrical system isn’t up to date anymore or something else, it quickly becomes more.
1100m² of land and 220m² house must also be managed and maintained first. For a 3 to 4-person family, that’s not necessarily needed.
Are there not smaller properties on more compact lots for a bit less money? With 450-500k you would have a pretty relaxed financing, allowing for a vacation or other expenses that come up without thinking too much.
Now you would have about a 2500€ installment plus surely 500€ operating costs in the place. You really have to want to spend 3k per month on living, even if, as said, it adds up financially for you.

Well, rent is probably significantly cheaper than purchasing the property. Purely in terms of the numbers, it fits.