Do I owe expiation for shortcomings in my work performance while working from home after being dismissed, or is my dismissal itself my punishment? And does the manager's forgiveness of my leave balance in exchange for his forgiveness of any shortcomings on my part absolve me before Allah?

You must repent to Allah by regretting what you have done and resolving not to return to the like of it. Part of repentance is to free yourself from the company's right. You have two options: either ask for forgiveness from the company owners, or compensate the company for the hours of absence from work. The reference for considering extra hours of work as compensation is the labor laws.