I use What's up Docker (https://github.com/getwud/wud) for this. It talks to the Docker daemon, is configured with labels. I get notifications when new versions and I can also look at a dashboard that aggregates all the updates and provides links to release notes.

Admittedly, I don't use Kubernetes, so I can't tell you whether What's up Docker supports it. A bunch of docker compose files is enough for me.

It can also update docker compose files with new tags for you, but I'm allergic to auto updates