Until recently when a bill was passed drastically changing how their retirement accounts had to be funded, the USPS was usually run for profit and was even usually actively profitable year over year. I think they’re still dealing with the fallout of that bill meant to hobble them, but I can’t imagine they’d operate at a loss purposefully.
The USPS even used to offer banking services which was also reported to be widely profitable until legislation was passed eliminating that service. Wouldn’t even be the first time that they had branched out beyond just mail.