The "why" is THE thing that needs to go in the git commit message. Capturing "why" is the entire point of that message and slapping a link to some external (and eventually absent) resource is not a good substitute.
1. Usually the commit message is often too short to capture the "why" adequately. 2. It is very beneficial to capture the why in one single source of truth, and that usually is not the Git commit message in a business context. Hate on Jira all you want, but if you capture the "why" there, you can add comments, view history, add rich context, link dependencies, add rich context, etc. Can't do that in a Git commit message.
For GH issues you can always navigate back to the PR discussion (which should have linked issues and other pointers in it) from the commit.
Of course when we switched to GH issues, we largely abandoned JIRA and years later the instance got turned off and deleted. Now all those JIRA tags are entirely useless.
IMO that actually argues for tight coupling between your issue tracker and your git repo. And what you really want is portability (which I don't see how you get other than with tight coupling). Ideally there would be open standardized formats, but as it is, github is the 800# gorilla that defines the format and as long as gitlab and other clones can slurp in github project metadata (or at least PRs) then that effectively gets you closer.
But any way... Fixed, immutable pointers to an Atlassian product that you might not be using in 5 years is not a good policy. I'd sooner accept the policy that the git commits needed to stand entirely on their own and all the information about the "why" of the change needed to be baked into the git commit or the comments in the source (I think that fails, though, since everyone is overly terse in git commits and summarizes issues and loses information--and the back-and-forth dialog in a PR discussion is useful because it contains more than just one person's voice summarizing the reason for the change).
Sorry to be nitpicky, but why did you abandon a tool that contained a lot of valuable knowledge? That's not the fault of GH nor JIRA, that's your fault. At least you'd back up descriptions + comments from these JIRA sources.
If you have somebody willing to write custom release messages, that's definitely better; but conventional commits is better than nothing for it.
[edit] At the bottom of https://scopedcommits.com/ I mean
If you're not using/tied to an issue tracker, embedding tags like these in git gives you some basic metrics.