The process which can be used is to have a generic repositories for all issues (it may also be easier to manage if we want a bot reporting new issues to our forum and/or channels/rooms discussions). In case it’s needed, some cases, issues can be linked to specific repositories by their owners. Also you can decide who can or can’t have access to issues. (read/write etc)
I’m not sure to get it, here are some interesting comparison between Bugzilla and Github issues from one of the links above.
Well, looking at the top distros in Distrowatch, CentOS and KaliLinux use MantisBT, Ubuntu use Launchpad (well distros based on Ubuntu mostly use launchpad), Debian the only one to use their own cgi-based BTS, Arch Linux use flyspray, MX Linux use Drupal, Manjaro uses Gitlab and Kaos and Antergos use Github.
The way Kaos organizes github for bug management is well documented by the way.
IMHO the main reason why developers of big distros don’t move massively to integrated environment is less because of the advantages rather than the amount of work (because they have a huge quantity of issues reported, may they be closed or open). We have the advantage or still being small.