The Tesla app allows Backup-only, Self-Powered and 2 Advanced modes. None of these allow you to automatically charge the battery at off-peak rates, power the house from the battery when needed, and export solar at peak exporting rates. To charge the battery you can manually set the Powerwall to Backup-only and then manually change it back to Advanced every day. Unfortunately, you cannot force the Powerwall to export excess solar, while still powering the house from the battery when needed, unless the battery is 100% charged.
It would be great if Tesla would add similar UI functionality of Peak and Off-peak in Advanced mode to Self-powered mode but with the options labelled as Import and Export.
If no Import/Export times are active then Self-powered will work exactly as it does currently.
If an Import time is active then the Powerwall will be charged from the grid and the house powered from the grid.
If an Export time is active then any excess solar power is exported to the grid rather than charging the Powerwall.
This should be fine with the power companies as grid power is not being arbitraged via the battery.
It is a relatively simple change for Tesla to make since all the base functionality is already in the app.