Do you mean the log from the Deploy tab of RStudio? It was pretty short:
Preparing to deploy application...DONE
Uploading bundle for application: 1135758...DONE
Deploying bundle: 2389083 for application: 1135758 ...
Waiting for task: 644953377
building: Parsing manifest
building: Building image: 2539484
building: Installing system dependencies
building: Installing packages
building: Installing files
building: Pushing image: 2539484
deploying: Starting instances
rollforward: Activating new instances
terminating: Stopping old instances
Application successfully deployed to https://myusername.shinyapps.io/OAqPCR/
Deployment completed: https://myusername.shinyapps.io/OAqPCR/
As I said, when I call Sys.getlocale(), it gives English_United States.1252 only, so I'm still puzzled where rsconnect takes something different...