Seems like Fossil is more like an alternative to GitHub than Git. Fossil not only tracks code changes but team chat, bug tracking, wikis, etc.
Fossil is an alternative to both git (source control) and github (issues, etc).
I think its brilliant having issues tracked in fossil. Part of the promise of github is that the user is in control, since your computer is a first-class citizen of a repository. You have all the code, and all the history on your computer. You can use github, but you don't need github, since its just another node in git's distributed network.
But that promise falls apart with issues and pull requests. Issues and pull requests don't get replicated by git. If github goes down, you can't interact with issues. If github ever turns evil, or you decide you want to self host git over ssh or something, you lose the history of all your issues and conversations.
Git is a distributed, replicated data format. Why are issues fully centralized? Its bizarre - You can have a project on both github and gitlab. And you can replicate commits to both. But you can't replicate issues using the same mechanism.
Fossil is far from perfect, but I think putting the issues and stuff into the repository itself is brilliant.
The desire to move off github (and therefore any additional services besides hosting you were using, which issues are just one -- new ones keep getting added to try and cement your dependence) is something more worthwhile of thought than the idea of github turning evil. Fortunately that desire is an actual thing that's very common, or at least the desire to not be wholly dependent, and is why many people don't even use github issues to begin with even if they use github itself for hosting (or some other non-issues features). So there's not a big problem, and even if you start with using github issues, there are various migration tools to move github issues out to [alternative]. (And of course github issues have their own merits, people frequently want to switch to them! So similar migration tools exist to move from [alternative] to github issues, I wrote one for Jira years ago.)
It is brilliant to integrate things with the decentralized source control itself, you get free backups and deciding to migrate to something different in the future is easy, I think it's an overlooked approach for a lot of people. (It seems less overlooked when it comes to documentation in various forms like developer-focused .md files, or broader full static html websites which github can conveniently host for you.) Fossil is well-worth investigating for this free integration to see if it meets one's needs. But of course nothing stops you from doing it with git yourself in various ways. For personal projects, I'm pretty satisfied with being as minimal as having an issues.md file and moving things to an issues-closed.md file when I close one. I've also used the git-issue extension (https://github.com/dspinellis/git-issue -- see also its bottom section of Related Work).
But despite its brilliance it's not always the right approach. It's very easy and reasonable to want more than what is realistic for something deeply integrated with the source code itself to provide, if only for inherent conflicts of desire, let alone any question of manpower. There are very good reasons to have entirely separate (and even multiple-of-kind partially overlapping/integrating/cross-referencing) systems for source code management, issue tracking, code review, forums, IM communication, wikis, public websites, docs (of whatever kinds and types for various audiences and authors, or public or not, or team-level spikes or plannings or retrospectives)... One aspect of Fossil I found weak was its user capabilities (https://fossil-scm.org/home/doc/trunk/www/caps/ -- no custom user categories alone is a deal breaker for so many things) but flaws in the execution of a fully integrated thing isn't really my point, my point here again is just that full integration despite its overlooked benefits and brilliance when applied to certain things is still not necessarily the right choice for something.