Why are there only 3 Thermostat-Modes available in Google Assistant if I enter them manually?
Without any custom modes there are 5 selection options.
Don’t really know. But this seems to be again an issue of the Google Home app.
Selecting by voice will work.
@michikrug! quick question if I may 
I found this website: https://developers.google.com/assistant/smarthome/traits/temperaturesetting
It lists additional temperature modes for google assistant.
Do you know by chance, if it’s possible to add those modes (or even others) to use with the google home app?
All Thermostat modes are already supported by the openhab integration.
Unfortunately, I have no idea how well they can be used with Google home or the assistant. This always differs a bit from the developer description.