I've tested this on both ArcGIS Pro 2.7.3 and 2.8. The Feature Class to Feature Class tool fails when trying to save the output to a file geodatabase (.gdb) on a mapped network drive (ubuntu server) in the .aprx project folder where I have read/write permissions. The tool only runs successfully my output location is a .gdb on the C drive or a microsoft network drive location.
Update: I believe the issue is related to the use of SMB3
SMB3 protocol weirdness - Esri Community
Supportibility for SMB3 on Samba backend - Esri Community
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