Best way to enforce manager check-ins across the org using M365 tools?

I think there are two ways you can go here. The first one would be the native DIY route. Microsoft Forms for a structured check-in template, Power Automate to send it on a bi-weekly schedule and capture submissions into a SharePoint list or Dataverse table, and Power BI on top for the leadership dashboard. 

The second way would be to take advantage of the 365 app ecosystem. It is what we decided to do after we realized we couldnt power automate and dashboard our way out of everything. You can definitely use Teamflect for everything you described. We started using it predominantly as a performance management tool but it has some pretty sleek meeting features with check-in forms, talking points and all that jazz.  It suggests regular 1-1s for managers and direct reports and tracks them well. 

Hope one of the two ways helps you out. Please mark as solution if it worked.