I figured it out... feel a bit dumb now, but here it is, if anyone experiences similar issues:
When I created my picture by pasting from clipboard, the new image is generated as a group, containing the pixel layer I wanted to work on. I had to expand the group and select the pixel layer (after selecting the pixel layer, the Flood Selection tool worked as intended), but selecting only the group without expanding did not let me make any selection, as descibed above.
Strg+A or Control+A is the shortcut for "select all" (working with Windows 10, Affinity Photo 220.127.116.11)... I tried this to check if I can maybe deselect / subtract portions of the image, but that didn't work either.