Docker – Rest Api doesn't return value after add PathPrefix in Traefik

I have 2 simple dockerized Rest Api apps which connect to external services and return json values. I try to deploy them behind traefik reverse proxy.

Here is docker-compose.yml for one Rest Api app:

version: "3.8"

services:
  first-rest-service:
    image: first-rest-service:latest
    container_name: first-rest-service
    restart: unless-stopped
    labels:
      - "traefik.http.routers.first-rest-service.rule=Host(`localhost`) && PathPrefix(`/first`)"
      - "traefik.http.services.first-rest-service.loadbalancer.server.port=8000"

networks:
  default:
    name: traefik
    external: true

Docker-compose.yml for second one app is almost the same (different image).
I try to deploy traefik as a reverse proxy. Here is docker-compose.yml for traefik:

version: "3.3"

services:

  traefik:
    image: "traefik:v2.10"
    container_name: "traefik"
    command:
      - "--api.insecure=true"
      - "--providers.docker=true"
      - "--api.debug=true"
      - "--log.level=DEBUG"
    ports:
      - "80:80"
      - "8080:8080"
    volumes:
      - "/var/run/docker.sock:/var/run/docker.sock:ro"

networks:
  default:
    name: traefik
    external: true

After run all docker-composes I can see every single Rest Api app with proper forwarding in traefik dashboard. But when I execute curl on traefik I cannot get proper value. Example:

curl http://localhost/first/api/version
> {"detail":"Not Found"}

But when I remove PathPrefix and try to expose one Rest Api service on traefik it works well. I change only this line in Rest Api docker-compose.yml file:

      - "traefik.http.routers.first-rest-service.rule=Host(`localhost`) && PathPrefix(`/first`)"

into this:

      - "traefik.http.routers.first-rest-service.rule=Host(`localhost`)"

Here is output from curl:

curl http://localhost/api/version

I get json with proper version:

{"version":"x.x.x"}

I was trying to use PathPrefixStrip, but probably I cannot use it in proper way.
Maybe do I need change something in Rest Api routers settings?