Relocate run.go and backup_integration.go to internal/ui #18
Description
Now that run.go is utilizing the tui package, we should organize the project structure by moving the run command logic and the backup integration helpers into the internal/ui namespace to better reflect their role in the architecture.
- Move run.go to internal/ui/run.go (or rename appropriately, e.g., internal/ui/runner.go).
- Move backup_integration.go to internal/ui/backup_integration.go.
- Update the package declaration in these files to ui.
- Update all import paths in the project (e.g., in cmd or main.go) to point to the new location in internal/ui.
- Ensure go.mod / go.sum are tidy if dependencies changed.