refactor(ui): move run command and backup helpers to internal/ui (#18)

[D3vanshC]

What this PR does

Moves the run command logic and backup integration helpers into the internal/ui namespace to better reflect their responsibility now that run depends on the TUI layer.

Changes

• Moved run.go → internal/ui/run.go (renamed where appropriate)
• Moved backup_integration.go → internal/ui/backup_integration.go
• Updated package declarations to ui
• Updated imports across the project to reference internal/ui
• Ensured go.mod / go.sum remain tidy

Result

• Clearer separation of UI-related logic
• Project structure better aligned with current architecture
• No change in runtime behavior