Just for clarification - SPT should not be installed inside your Live Tarkov folder, it goes in to its own folder either on the same drive as your Live Tarkov or on a different drive with space available. If you have already done this, fantastic!
I took a second to look at the logs specifically the Server Log, are you making any changes to your profile whilst the sever is running? Are you opening and closing your Launcher and/or have multiple open at the same time? I'm asking so I can get more information on your issue whilst doing a little troubleshooting to narrow things down so we can help fix it. It sounds like something isn't where it should be or hasn't been setup correctly, hopefully you can provide more info.