You are using SFTP. OpenSSH SFTP server cannot move files across file systems. If you want WinSCP to use mv shell command, use SCP protocol. Or you can add a custom command to WinSCP, if you want to use mv shell command, while in an SFTP session.

Yeah, you are correct. My /tmp and /home mounted as different partitions:

But why WinSCP can't just perform mv /tmp/ca.cer /home/ in such situation? It is better than just fail.

As the error message suggests, most likely the cause is:

Moving a remote file to a different filesystem (HDD)

See also https://winscp.net/eng/docs/sftp_codes#code_4

When I trying to move any file from /tmp to /home I got "general failure, error code 4". Though copying the same files works fine. I attached video demonstration and log.

FYI Log was collected separately from attached video, thus this log shows only events from connecting to server to appearing of the error.