Sadly, GitHub doesn't store its value-add assets within the repository itself; so all of the PR conversations, Gists, Issues, and so forth aren't within git itself.
It's the way the open source options work too (GitLab, Gitea, Forgejo), and they don't have any sinister motive for that—it's just easier to build that way.
This speaks to one of my secret desires, I've worked at a bunch of small companies now where the workflows were all ad-hoc and I feel like even at bigger companies there are persistent failures to "understand Git"... one of the most pernicious being that, most companies have a modernist "this is prod, it is one place running one codebase" approach, Git is postmodernist "here is this project, there are many branches showing different perspectives on what this code could be", most CI/CD systems in my opinion sit at the interface between these and choose the wrong side to be on, they choose the Git side -- "we ask every branch, 'do you want to deploy yourself to prod?' and if it says yes by virtue of having a CI.yaml file with a branch filter naming itself to be run, then we deploy it to prod."
So what I want is kind of to build a company that's just strongly opinionated about that... "everything is in one Git repository, the `main` branch is authoritative for ACLs and CI/CD config, the bugtracker writes issues directly into that repository and has an ACL role that allows it to do that, the RFC widget writes your code design docs directly in there as well, we do rebase but we merge without fast-forwarding, you have to use semver and it works like this..." and probably nobody will use our offering because "GitHub is more trustworthy" but "if anybody does they'll love us" haha
I realize you're talking about git, but I think it's also pretty important to have a place where users can submit issues and dev's can say "it's fixed in version XYZ", these are not features of git.
You can host your own on your own site. Most major open source projects have their own website anyhow. They really don't need to be on github or gitlab to begin with, just roll it yourself like the rest of your website. The only reason why people do it is because its a meme at this point to have a github (and even gitlab, if only as a foil to github).
Rather than making it a feature of git, it would probably be sufficient to have a tool that packed issues and PRs from the forge into the repo (in preparation to be migrated) and then unpacked them into the forge's API on the other side.
Fossil lets you synchronize artifacts both ways, so you can clone a repo, participate in discussions when on a plane, write some replies, connect back to the internet and sync them back up to the server.
When your server goes down, you don't lose anything. There's no need to remember to back up your issues every day, every time you clone the repo, you also clone its tickets, forum, wiki etc.
Fossil doesn't have a good story around cross-repo authentication (without separate per-repo accounts), CI/CD, 2FA, SSO support and such. It's a great tool if you're writing a single personal project with little regard for security, but that's about it.
You can use ChiselApp.com (which I maintain) to host your Fossil as well, and since every clone has the same data (minus passwords) it's trivial to migrate.
Why do you need a centralized hub? Most repos on github are entirely unrelated to eachother. Repos can be self hosted. Issues can be tracked on your own website. You don't need a megacorp to run a website. If you are writing open source tooling you are more than qualified to roll your own here.
Cloudflare, AWS, Azure, Google Cloud and Whatever-is-used-by-China: people make fun of the IBM guy who said "the world has a market for maybe 5 computers", but he was right all along...
