There is a GitHub for government [0] but it relies on contribs and isn’t very complete.
GSA started code.gov under the Obama administration with the aim to create a single index of all government projects. It withered under Trump and was basically defunded under Biden so they don’t really do much other than link out to major agencies and there’s no longer a requirement to timely index.
My org has like a 1000 repos and we’re one of hundreds of agencies so I can’t imagine collecting all these together without a little effort. The original code.gov worked pretty well as everyone just dropped a code.json file onto their web site and GSA scooped them up and combined them into a single. So it’s a real shame they stopped doing that, and stopped asking people to publish their code.jsons as it was a good idea.
Merely as a point of reference, https://github.com/orgs/microsoft/repositories cites they currently have 6100 repos with another 2200 in /orgs/Azure so 10000 in an GH org wouldn't be unprecedented. I couldn't readily find any way to cough up their other top-level brands, and the "topics" seem to apply only to the repos themselves, not to the GH Organizations
My point stands though as it’s really impossible to try to standardize an organization as massive as a government into a single code management system, much less a single org, even if it has fantastic hierarchical management.
The government can host their own GitHub instance if they want to. I think the point is that there are probably thousands of “servers” with government repos. And consolidating to one “server” is a horrible idea.
A catalog is good though.
But for a universal (any host, any government) dataset contributing to wikidata would be helpful, and in the fullness of time I'd like to use that to cross-validate and identify missing entries https://github.com/github/government.github.com/issues/877 but the properties available probably need work to get there, right now there's e.g., https://www.wikidata.org/wiki/Property:P1324 https://www.wikidata.org/wiki/Property:P2037 https://www.wikidata.org/wiki/Property:P8827