Apparently this works using something called SST as a wrapper around CDK:
https://garden.mirahi.io/deploy-a-nuxt-3-application-on-aws-using-sst-serverless/
Haven't tried it.
Alternatively, maybe this:
https://blog.canopas.com/how-to-configure-ssr-in-nuxt3-and-deploy-it-with-serverless-architecture-f86e63ae8b8d