EKS managed node groups do not support setting tags directly (
https://github.com/aws/containers-roadmap/issues/608).
A possible workaround here is creating a custom launch template and passing that to the node group. In that launch template you can set the tags and configure them to be propagated to instances. (Note: You do not have to set all options in the launch template, EKS will merge in its defaults).
This issue tracks automating this workaround on the pulumi side:
https://github.com/pulumi/pulumi-eks/issues/658. Please upvote it if you're interested in it, this will help us prioritize it