What tool or type of tool am I looking for?
Jenkins can work just fine for this purpose.  In my view, Jenkins is a general-purpose automation tool, not necessarily a CI/CD tool specifically.
I'm on an Ops team and we use both Jenkins and Rundeck.  We generally prefer Jenkins because we find it difficult to navigate the Rundeck UI and find things like job output, but on the other hand it's often easier to write jobs for Rundeck, because you don't need to know Groovy/Pipeline.  Here are some examples of what we use each for:

Install package updates on managed systems (yum/dnf packages) - Rundeck
Deploy &amp; provision new VMs - Jenkins
Run Chef on managed systems - Rundeck
Clean up stale Computer objects in Active Directory - Rundeck
Clean up stale subscriptions in Red Hat Satellite - Rundeck
Create &amp; configure new repositories in Bitbucket from templates - Jenkins
Build new vagrant images - Jenkins
Backup &amp; upgrade some services that my team manages (AWX, Red Hat Satellite, etc.) - Jenkins or Rundeck depending on the service

I'm not claiming that either of these tools is the best choice for any of these particular examples, just that my team uses them for these purposes and they generally work well.  Historically, which tool we use for each job generally has come down to personal preference of the person who created the job.
In terms of the name of this type of tool, we just call them &quot;automation tools&quot; or &quot;automation platforms&quot;.  I'm not sure if there's a more &quot;industry-standard&quot; term for this type of tool.