Remember that Git is a distributed VCS, so no git repo is dependent on a central server. Everything else about the project might be heavily dependent on GH, but any active developer is going to have a full copy of the code with history on their main workstation.

That being said, it highly depends on the project, but I'd put it into a few buckets.

1. Un/barely maintained projects - This is by far the largest number of repos, and many of them are used as dependencies by all sorts of projects. The truly unmaintained ones would vanish, and I bet most of the barely maintained ones would as well. The most important of these would probably be resurrected since their code will be sitting on all sorts of drives, but it will be a mess. Take a look at https://nesbitt.io/2026/05/08/weekend-at-bernies.html for an idea.
2. Small individually actively maintained projects - There are a lot of these and many of them could continue to be just fine, depending on how much of the full GH feature set they use. They would lose all the PRs, wiki spaces, discussions, issues, and maybe even the project page itself that are hosted on GH. For most projects it would be an annoyance to have lost all that, but if it's a small enough project that one person is maintaining it, it's probably small enough to pull over to something else reasonably easily depending on how all in they are on GH tools and their use of type 1repos. And a project with only one main contributor is unlikely to fragment.
3. Mid-sized active projects - Probably the hardest hit. A lot of these are all-in on the GH tools, particularly issues and CI. Losing that would hurt a lot because the project is big enough to really need those tools and uses them at a volume that they can't just host on the leads laptop. These are also going to take a lot of work to set up the project infrastructure elsewhere. And this would probably be the sort of thing to push and simmering tensions to erupt, leading to fragmentation.
4. The big projects - Probably the least hardest hit. Most of these are just using GH as a push mirror. The core team probably has a functioning private communication and governance system, their own issue tracker (even if it pulls from GH), documentation, and public discussion groups. Most of these run their own private CI. And they are the ones most likely for another host to step in and offer to help.

So the little stuff? Probably going to be annoyed or not care a lot. The big stuff? Same thing. But that middle group would be hurt.

Then projects move their repos somewhere else which is pretty easy with git.