Hi @stk,
For my institution, I'm the primary Canvas administrator, and have the title "Coordinator of Digital Education". The "Office of Digital Education" (my home) is part of the Office of the Provost here. Our teaching and learning center (where Instructional Designers are housed) is also part of the Provost Office. Our IT department calls under the Chancellor's Office.
There was a time where Digital Education and the leaching and learning center were merged on paper, but it didn't really change much other than reporting lines. Digital Education is really a somewhat unique blend of a bit of instructional design, plus a bit of IT.
In hearing from other Canvas admins at various colleges, it seems like there's a pretty even split between Canvas admins being house in the IT area and in some division of academics (usually the Provost Office, sometimes with the teaching and learning center, other times a separate division).
I do have a Computer Science degree, so I do a small amount of coding (mostly customizing small things via JS/CSS, but I also created a "cleanup" type python script we run on a daily basis to catch oddities in Canvas courses/users/enrollments/etc. As the main admin, i'm basically tire-2 tech support for Canvas on our campus (each college has an employee who is the tier-1 front line support, and escalates things they can't figure out to me. I am also involved with strategic planning around online/digital education, and creating/revising related policies. I am not trained in Instructional Design, but I have picked up quite a bit being in this job, and will definitely give some technical advice around course design if I'm asked. It's a very interesting blend of work.
Hope this helps you out a bit!
-Chris