Why were rotary vane compressors never used in jet engines?
The most important characteristic for a jet engine compressor is high mass flow rate with light weight and if possible small size. For the same size, the flow rate can be increased by operating the compressor at higher rpm. But sliding components don't allow that.

Only the axial and centrifugal compressors can achieve sufficient flow rates, so they are used. Centrifugal compressors achieve higher pressure ratio for weight, but are larger, so they were used in many early designs and now remain in small turboprops while larger engines use axial compressors for their compactness.