Since Emissary-ingress's configuration is entirely stored in Kubernetes resources, upgrading between versions is straightforward.
Migration is a two-step process:
Install new CRDs.
Before installing Emissary-ingress 3.8.1 itself, you need to update the CRDs in your cluster. This is mandatory during any upgrade of Emissary-ingress.
Install Emissary-ingress 3.8.1.
After installing the new CRDs, upgrade Emissary-ingress 3.8.1.