Trying to set up PIA with OVPN client (docker)
As I can see in your logs you've received Inactivity timeout (--ping-restart), restarting message after successfull connection in short period of time.
I had the same issue.My client successfully connected and in few seconds (20-40) has been restarted.In my case I've actually run two clients with the same client name (CN) on different hosts.
To fix it I've generated different clients for each host.
For me, the problem was using default PIA config. Once I switched to OPENVPN CONFIGURATION FILES (STRONG), the problem was gone.
You can find the configs at https://www.privateinternetaccess.com/helpdesk/kb/articles/where-can-i-find-your-ovpn-files-2, and if the link goes down, try googling "pia config".