From their blog post (linked to by the docs page) about self-hosting:

The following Omnivore features will not be included in this minimal Omnivore setup:
- The web app (we will use the iOS app from the AppStore as our client)
- Search of PDFs
- Saving URLs instead of pages (more on this below)
-Receiving newsletters via email
- Text to speech

Not only that, they use a non-self hosted elasticsearch provider.

Their example docker-compose file in the repo has no less than four containers defined, not including the database server, and you have to build them all yourself, so it's more of a local dev environment type deployment rather than production.

Here's their "make self-hosting more practical" Github issue, coming on two years old with no progress: https://github.com/omnivore-app/omnivore/issues/25

All of that was more than enough for me to not even bother to try to deploy my own instance. I manage with Wallabag for now, it's not the greatest implementation either but at least it can be self-hosted. Omnivore looks slick but the backend just doesn't keep up.