If you look at the STL, the hole for the nuts on the Delta stage illumination mount is different from the equivalent hole on your recent Microscope build.
The Microscope version 7 uses an updated hole shape that is designed to print without so much stringing in the hole. The Delta stage is largely based on the V6 Microscope design and has not yet benefitted from the improvements in V7.
The interim solution as you have found is to scrape out any stringing before inserting a nut. It is something that we would like to avoid in future updates of the Delta stage.