After writing the below, my hypothesis of the underlying cause is that the HHVM cluster is not running the right code, since all of the affected edits are also tagged with HHVM, so I'm CCing Ori.
English Wikipedia is on 1.25wmf2. GettingStarted 1.25wmf2 includes
"Remove unused code/messages" (https://gerrit.wikimedia.org/r/#/c/161969/) (you can tell from the "Included in" and from https://git.wikimedia.org/log/mediawiki%2Fextensions%2FGettingStarted.git/refs%2Fheads%2Fwmf%2F1.25wmf2
Part of that change is removing the edit tagging functionality. However, this doesn't appear to have taken full effect, since some edits are still being tagged (https://en.wikipedia.org/w/index.php?title=Special:RecentChanges&tagfilter=gettingstarted+edit).
GettingStarted no longer has any edit-tagging functionality as of that commit (nor on master) (ChangeTags appears nowhere).
So I am theorizing it might be a deployment issue, hence CCing Greg.
There is also a minor, but slightly weird thing:
GettingStarted 1.1.0 (03c83f1) 08:39, 2 October 2014
That is the commit right before the branch cut.
However, https://git.wikimedia.org/log/mediawiki%2Fextensions%2FGettingStarted.git/refs%2Fheads%2Fwmf%2F1.25wmf2 shows the standard "Creating new wmf/1.25wmf2 branch". That commit doesn't change the actual code, but I still don't really understand the discrepancy.
Version: wmf-deployment
Severity: major