Are these things really so "stupid" and can't handle excess energy any other way?
As said. If it is a drainback system, the collectors empty as soon as the set maximum storage temperature is reached. So no problem. If it is a classic "pressure system," the solar fluid eventually evaporates at high temperatures and goes into the solar expansion vessel. At first, nothing serious happens, but if this process repeats several times in summer, the solar mixture cracks and may possibly clog the system. In addition, the mixture of water and propylene glycol then breaks down and frost protection is no longer uniformly ensured. Therefore, for pressure systems: when in doubt, use less collector area.
Wouldn't the device override my set desired temperature and keep heating in case of oversupply of energy? What exactly happens?
No, the sensor of the gas device is located above the sensor of the solar system. Typically, you set about 50° C target temperature (+/- x) on the gas device; so if the solar system has already brought the storage above 50°C (the solar heat exchanger is located at the bottom of the storage), the gas device does not even switch on.
What about heating support through solar thermal? Does that make sense?
See Nordlys, it does not bring much; especially with your roof: heating support in your house with solar brings—if at all—some effect at 45 to 60° collector inclination. During the heating period, the sun not only shines for a shorter time but also stands lower. My advice remains: ideally a 300 l storage tank (not much more expensive than a 190 l) and only 2 collectors, so you probably meet the KfW requirements and, in the case of a pressure system (which are the vast majority in Germany), have overtemperature in summer as rarely as possible.