Use relative paths in UI and file logs

[Tosox]

Task Description

As a user, I need installation log messages to display relative paths instead of full absolute paths so that logs are less cluttered, easier to read, and don't expose sensitive system path information. The file logger should log the working directory once at startup so full paths can still be reconstructed if needed.

Acceptance Criteria

• Installation log messages in both the UI and file log use paths relative to the working directory
• The file logger logs the absolute working directory once at program startup
• UI log messages are not cluttered with long absolute paths

Additional Information

Relevant code: path logging throughout ModEntryInstaller.install() and InstallCoordinator.runInstallation()