Folders and files:

%ProgramData%\Veeam\Backup                                    # Logs folder
%ProgramData%\Veeam\Setup\Temp                                # Installation and Upgrade
%UserProfile%\AppData\Local\Veeam\Backup                      # Backup & Replication Console
%ProgramData%\Veeam\Backup                                    # Jobs, Components and Services
%ProgramData%\Veeam\Backup\<jobname>                          # Jobs, Components and Services
%UserProfile%\AppData\Local\Veeam\Backup\VeeamPowerShell.log  # PowerShell

Folders:

/var/log/VeeamBackup
/tmp/VeeamBackup

https://helpcenter.veeam.com/docs/backup/vsphere/exporting_logs.html?ver=120

https://www.veeam.com/kb1825