Routing to new container for every session

it's my first post, so I hope it is in the right place.

I would like to have auth (e.g. OIDC) on traefik and then every session proxied to a new container (on Kubernetes or Docker).
I'm aware of performance drawbacks, etc. This container has just some webapp.
Containers should be dynamically created for every authenticated session and then deleted after use.
Do you think I can set it up using traefik or do you have any idea what tool can be used? I see scaling of generic product insufficient.

Each route consists of a name (limited to 63 characters),