The original problem of not being able to send data to child sites has now indeed disappeared.
However, I also do not see any changes to my child sites after saving the keys I made to them.
I looked in more detail to the keys I made and then imported (following the steps in these videos: https://youtu.be/yJTSApmeXJs and https://youtu.be/D2eSxjXbras). And it looks like the settings fields are not at all copied by the key maker:
This is the result of my attempt to make a key for the settings of Broken Links Checker:
And the same for my attempt to make a key for the settings of WPvivid:
In the example videos you see all the fields from the settings form being included in the key, but my keys just have this one field. So I think that may explains why I don’t see changes to my child sites…the fields from the settings page have not actually been copied in the key. No idea why not…