As of v2.107.3-2 the Jenkins dogu comes with pre-configured git tool (/jenkins/configureTools/) but not with mercurial.
Good to know: We have a fully working hg for alpine on the PATH!
Quick fix: Manually create a mercurial installation like so:

Note that the Use Repository Caches flag is required to be able to use Mercurial in Pipeline build jobs, as described in JENKINS-47040.
Otherwise, this would result in ERROR: No configured Mercurial installation.
However, it would be way more intuitive, if this would come pre-configured with the Jenkins dogu.