The license is not the issue, the use is
Holding a commercial license does not by itself change your personal auto policy. What matters is what you are driving and for what purpose at the moment of a loss. A personal vehicle used personally is covered normally, whatever is in your wallet.
The employer’s policy covers the employer
Driving a company truck is generally covered by the company policy, and that cover is arranged for their benefit. It may protect you as a driver and it is not yours, and it ends when the shift does. Relying on it for anything personal is a mistake.
Driving someone else’s vehicle leaves a gap
Where an employee regularly drives vehicles they do not own, there can be exposure above the employer’s limits that falls back on the individual. For a household without a personal vehicle of its own, that gap is worth understanding rather than assuming away.