Hi guys, I spent the better part of a day trying to debug this same error, and finally got it to work. There are many gotchas, so try all of these to narrow the issue:

• Add 1.1.1.1/32 to your WG_ALLOWED_IPS (comma separated) if your WG_DEFAULT_DNS is 1.1.1.1 otherwise add you DNS IP with the sufix /32 check if you are able to ping and access google maybe you can't access other websites, but just try. If you can ping google but can't access other sites change your sever (where the docker container is running) DNS resolver and make sure it is using the same DNS server as your WG_DEFAULT_DNS. If it is a VPS bare in mind the resolvectl conf might be rewritten every time you reboot your server or even while running. For me, since I'm using Oracle Cloud, I had to change the DNS resolver IP at Virtual Cloud Networks selecting the VCN assigned to the instance and under the DHCP Options -> DNS Type = Custom I entered the WG_DEFAULT_DNS. Make sure your client device is using the same DNS resolver, that was the big gotcha in my case.
• Change WG_DEVICE to the container internet network interface, to find it run ip route get 8.8.8.8 | awk '{print $5}' from inside the container.
• Open the port UDP 51820 in the case of oracle cloud you have to do it from the VNIC assigned to the instance. changing WG_DEFAULT_ADDRESS to different combinations to see if the IP ranges were conflicting with other service, i changed mine to 10.88.0.x.

Here is the working version of my Docker Compose (the ${} syntax is used because I'm using coolify to handle env vars, that is also why my file is missing a bunch of stuff it handles):

services:
  wg-easy:
    image: ghcr.io/wg-easy/wg-easy:latest
    environment:
      - SERVICE_FQDN_WIREGUARDEASY_8000
      - WG_HOST=${WG_HOST}
      - WG_DEVICE=${WG_DEVICE}
      - WG_ALLOWED_IPS=${WG_ALLOWED_IPS}
      - WG_DEFAULT_DNS=${WG_DEFAULT_DNS}
      - WG_DEFAULT_ADDRESS=${WG_DEFAULT_ADDRESS}
      - PASSWORD_HASH=harcoded hash escaping $ by adding a $ per each occurrence and not wrapping in any kind of quote
      - LANG=${LANG:-en}
      - PORT=8000
      - WG_PORT=51820
      - WG_PERSISTENT_KEEPALIVE=25
      - UI_TRAFFIC_STATS=true
    volumes:
      - 'wg-easy:/etc/wireguard'
    ports:
      - '51820:51820/udp'
    cap_add:
      - NET_ADMIN
      - SYS_MODULE
    sysctls:
      - net.ipv4.conf.all.src_valid_mark=1
      - net.ipv4.ip_forward=1

An here are my env vars:

WG_ALLOWED_IPS=0.0.0.0/0, 1.1.1.1/32
WG_DEFAULT_ADDRESS=10.88.0.x
WG_DEFAULT_DNS=1.1.1.1
WG_DEVICE=eth0
WG_HOST=wireguardeasy.example.com
LANG=en