It depends on the software and situation of course, but if you are paying a contractor to develop/write a solution for you aka "government built" then the contractor that writes the code owns 0 of that code. It's as if it was written by Uncle Sam himself.

Now, if the government buys software (licenses), the companies will retain ownership of their code. So if Uncle Sam bought Service Now licenses, the US doesn't "own" service now. If service now extended capability to support the govt, the US still doesn't own the license or that code in most cases.

Sometimes the government will even pay for a company to extend its software and that company can then sell that feature elsewhere. The government doesn't get any benefit beyond the capability they paid for--ie they don't own that code. That can work to the governments benefit though, because it can be used as a price negotiation point. "we know you can sell this feature to 50 different agencies if you develop it for us, so we only want to pay 25% of what you priced it at".

But like it said, if it's a development contract and the contractors build an app for the government, all of the contracts I've ever seen, have Uncle Sam owning it all. The govt could open source it if they wanted and the contractor would have no say.

That's what we call GOTS products https://en.m.wikipedia.org/wiki/Government_off-the-shelf#:~:text=Government%20off%2Dthe%2Dshelf%20(,for%20which%20it%20is%20created.

Vs COTS:

https://en.m.wikipedia.org/wiki/Commercial_off-the-shelf

With COTS, that's where you'd see the ownership (depending on the contract/license agreement of course) remain with the vendor.