The moment of enlightenment came in the morning, as I rode my bike to catch the 7:26 train. So silly...
My bad habits from old Sigil work flow! This new python Sigil needs to be actually installed for QtC to run it!
So as soon as I could - some 12 hours later - I opened QtC and clicked [Project] item (fifth down on the left - see pictures), there under "Build Steps" [Add Build Step]->[Make] just checked box by "install" item. Just for a good measure "-j 4" by the [Details]-"Additional arguments" for the first build step (make) to use my four cores.
Now click on the green arrow and...
and...
.
.
.
Spoiler:
Sigil runs of course

.
Now would be perhaps good time to do some real work?
to be continued...?