feat: Improve logging throughout the Dynamo path

[gs-olive]

Description

• Add clear logging at the beginning and end of each phase of compilation
• Reword logging in certain locations for clarity

Addresses #2399

Type of change

• Documentation and logging improvement

Checklist:

• [ x ] My code follows the style guidelines of this project (You can use the linters)
• [ x ] I have performed a self-review of my own code
• [ x ] I have commented my code, particularly in hard-to-understand areas and hacks
• [ x ] I have made corresponding changes to the documentation
• [ x ] I have added tests to verify my fix or my feature
• [ x ] New and existing unit tests pass locally with my changes
• [ x ] I have added the relevant labels to my PR in so that relevant reviewers are notified