I'm using dockerized Airflow based on 'puckel/docker-airflow:1.10.9' image.
docker-compose file is the following:
version: '3.5'
services:
  postgres:
    image: postgres:12.3-alpine
    environment:
      POSTGRES_DB: airflow
      POSTGRES_USER: airflow
      POSTGRES_PASSWORD: airflow
    ports:
      - 5432:5432
    volumes:
      - ./data/postgres:/var/lib/postgresql/data
  webserver:
    build:
      context: .
      dockerfile: docker/development/webserver/Dockerfile
    restart: always
    depends_on:
      - postgres
    environment:
      ...
    volumes:
      ...
    ports:
      - 8080:8080
    command: webserver
    healthcheck:
      test: ["CMD-SHELL", "[ -f /usr/local/airflow/airflow-webserver.pid ]"]
      interval: 30s
      timeout: 30s
      retries: 3
Connection to MySQL on host is required in one of the tasks in DAG.
Connection details are the following:

When I'm trying to trigger DAG, the task instance fails with _mysql_exceptions.OperationalError: (2006, "Unknown MySQL server host 'host.docker.internal' (-2)")
I've tried the same as in this issue, but the problem still persists.
Also, here are some failed docker network checks:
$ docker run --rm webserver ping 'host.docker.internal'
ping: bad address 'host.docker.internal'
and
$ docker run --rm alpine nslookup host.docker.internal
Unable to find image 'alpine:latest' locally
latest: Pulling from library/alpine
df20fa9351a1: Pull complete 
Digest: sha256:185518070891758909c9f839cf4ca393ee977ac378609f700f60a771a2dfe321
Status: Downloaded newer image for alpine:latest
Server:         192.168.100.1
Address:        192.168.100.1:53
** server can't find host.docker.internal: NXDOMAIN
** server can't find host.docker.internal: NXDOMAIN
 
    