I read that with Image ⇾ Mode ⇾ Indexed I can get the whole image black and white without grey, but how to only apply this to a selection, other than copy the selection out – apply – paste back?
Just make a selection and use the Threshold tool on it:
Note that when doing so you have no fine control on which colors become black and which become white, so a more complete solution is to convert to monochrome first (
Colors ➤ Desaturate ➤ Desaturate or
Colors ➤ Desaturate ➤ Mono mixer) before applying the threshold.
You can do this with the G'MIC Filters that come as a plugin for Gimp. These filters are applied to a selection if there is one. Below is using the filter Black & White > Stamp: