Traefik also supports running on K8s, yes.
On that note, if you're moving to K8s, I recommend looking into K8s Gateway API, it's the successor to the old Ingress API. There are other, more complete, implementations of it than Traefik. See https://gateway-api.sigs.k8s.io/
I'm using istio (in ambient mode, so it doesn't put its sidecar into every pod I create), and Nextcloud behind it, works flawlessly. It does consume a bit of time to set up properly though.
TLS certificates are handled via cert-manager, which works with both Ingress and Gateway API, independent of which implementation you choose.
I've also tried envoy gateway (had issues with uploading larger files via Nextcloud Web UI and Gradle publish to maven repo).
Cilium (a CNI) also has an integrated Gateway and Ingress API implementation, works fine, but lacks some of the most recent stable features, and quite some experimental features. But if you just need a HTTPS gateway without much fuss, it's rock-solid. Setup time is also minimal for the Ingress/Gateway controller part. Cilium CNI on the other hand takes a lot of time to understand and configure, if you're unfamiliar with networking in general.
Traefik's featureset is comparable with Cilium's Gateway API implementation, also works, simple to setup, and might be better suited, if you're already familiar with it using docker, as it's the same concepts, just slightly different config (docker labels vs. Ingress/Gateway API with Traefik specific annotations).