Alan Lee the latest release of the GitHub plugin (1.29.3) depends on git plugin 3.4.0 or newer. The GitHub plugin expects the git plugin to write BuildData.
All releases of git plugin 3.x write BuildData. Git plugin 4.0.0-beta10 (pre-release delivered July 5, 2019) and git plugin 4.0.0-beta11 (pre-release delivered Sep 13, 2019) write BuildData.
Git plugin 4.0.0-rc (pre-release delivered Jan 30, 2019) does not write BuildData. Git plugin 4.0.0-rc was a failed attempt to resolve the memory bloat caused by the git plugin (JENKINS-19022). The attempt introduced too many incompatibilities and had to be reverted. My sincere apologies that I released git plugin 4.0.0-rc. The poor choice of version string caused it to appear in the Jenkins update center rather than in the Jenkins experimental update center.
If you are running git plugin 4.0.0-rc and cannot downgrade, then I assume that means some plugin in your installation has declared a dependency on git plugin 4.0.0-rc. That plugin needs to be updated to not depend on git plugin 4.0.0-rc. The BuildData related changes in git plugin 4.0.0-rc are not included in git plugin 4.0.0-beta10 and are not included in git plugin 4.0.0-beta11 and will not be included in the final release of git plugin 4.0.0. The git plugin 4.0.0-rc release was a terrible mistake that I made which delivered pre-release code to the production Jenkins update center. The git plugin 4.0.0-rc release was also the clear proof that the API changes proposed in git plugin 4.0.0 pre-releases introduced too much incompatibility for other plugins that use the BuildData provided by the git plugin.
If you cannot downgrade because an installed plugin has an explicit dependency on 4.0.0-rc, then you should still be able to upgrade to git plugin 4.0.0-beta11 from the experimental upgrade center. However, if one of your installed plugins truly has a dependency on git plugin 4.0.0-rc, it seems likely that the reason it depends on git plugin 4.0.0-rc is because it is using the API changes that were included in git plugin 4.0.0-rc. Those API changes are not available in newer pre-releases of git plugin 4.0.0 like git plugin 4.0.0-beta10 and git plugin 4.0.0-beta11.
In summary, if you cannot downgrade because one of your plugins explicitly depends on git plugin 4.0.0-rc, then that plugin must be changed to not depend on git plugin 4.0.0-rc. If you cannot downgrade for some other reason, then you can likely upgrade to git client plugin 3.0.0-beta11 and git plugin 4.0.0-beta11.