When building the attached qtbug71551-qbs.zip with a statically-built Qt, all shader effects are missing. The symptoms are identical to those seen in
QTBUG-67429, which was the issue that motivated me to start building statically on Linux in the first place. An identical project built using qmake with a statically-built Qt doesn't exhibit these issues.
In the screenshot above, there should be a drop shadow under the tool bar, but it's missing.