Taking a look at your docker-compose.yml I see this volume mount:

volumes: 
- /volume1/SN/Docker/searxng-stack/searxng:/etc/searxng:rw

Whereas /volume1/SN/Docker/searxng-stack/searxng is the directory on your system docker is attempting to use to store the files inside the container from /etc/searxng.

Example of a volume mount that’ll likely work better for you;

volumes:
- ~/docker/config/searxng:/etc/searxng:rw

The tilde (~) acts as your current users home directory (aka: /home/YourUser) not owned by root and where docker persistent volumes should be stored.

After making the change over to that directory and configuring SearXNG how you like re-create your docker container with sudo docker compose up -d —force-recreate

Apologies for the poor formatting, typing this on mobile.

Edit:

Note: if you want to expose the port do not add the 127.0.0.1 like how I have in my docker-compose.yml.

have you checked the directory & file permissions with ls -la /Your/SearXNG/WorkingDir ?

The error in your log is telling you that the container does not have permission to that directory/file, you can essentially bypass this with sudo chmod 777 /Your/SearXNG/WorkingDir/* and sudo chown 1000:1000 /Your/SearXNG/WorkingDir/*

However, if you’re looking for security best practices this is not advisable but if all you care about is that it works it should be fine.

Late to the party but I decided to pickup a 13th gen ASUS NUC with an i7 over a prebuilt NAS, bought a couple external hard-disk bays setup Proxmox running a headless Debian 12 VM and almost everything runs great however, mistake was using Debian 12 because the Linux kernel is pretty far out of date and does not support the CPU properly.