What about deploying prebuilt docker image on dedicated server?

What about it? It can be easily done with Ansible. I managed a distributed infra with containers orchestrated by Ansible, worked fine.

it would be much less moving/fragile parts in prod. I am not an expert in this topic, and trying to learn about different approaches.

This amazing playbook spins up a ton of dockers:

https://github.com/spantaleev/matrix-docker-ansible-deploy

(I haven't used it in a few years, when I tried to deploy OpenStack with it, so if this is outdated, please, correct me!)

Ansible is imperative, it can work toward a static state, and that's it. If it runs into a problem it throws up its SSH connection, and cries tons of python errors, and gives up forever. Even with its inventory it's far from declarative.

k8s is a bunch of control loops that try to make progress toward their declared state. Failure is not a problem, it'll retry. It'll constantly check its own state, it has a nice API to report it, and thanks to a lot of reified concepts it's harder to have strange clashes between deployed components. (Whereas integrating multiple playbooks with Ansible is ... not trivial.)