What are the names of the interfaces for the usual device manufacturers?
At BSH there is Home Connect. At Samsung it is called Smart Control, etc. But you can adapt any device. The simplest option is the switchable socket. That already existed in grandma's time with a mechanical timer in between. Nowadays, this can be controlled automatically and on demand. For example, your dishwasher cleans the dishes during the day when you are at work and only when the photovoltaic system has a surplus (provided it actually supplies power). Of course, normal operation is still possible and your devices will not be restricted.
Do I absolutely need a battery? Such a storage is supposedly not economically worthwhile...
No, you don’t necessarily need one. Especially without storage, you can prefer to use the electricity directly and power your devices with it.
Does that mean there is a setting in the menu/program selection of the dryer? I have never seen that.
Tassimat meant simple devices without much frills. You set them beforehand by switch as you need them, and as soon as the device gets power via the switchable socket, the program starts. The command is given to the socket, for example, by any energy management system or directly from the photovoltaic system or the resident or whatever.
What is meant by "switchable socket"? How is it switchable? WLAN? Via an app on the phone?
You can choose how it is controlled. Timers, apps, phones, displays, completely autonomous and automatic, by gesture, voice, or smoke signals. The possibilities nowadays are almost limitless.
Even coordinate-based control, i.e. based on your location, is no problem.
You just pick a suitable way. Preferably without any cloud or other nonsense.