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