I have tried to reproduce the same in my environment and got the positive results.
Note: In this demo, I have tried to bind index.html file to /usr/share/nginx/html folder to identify the changes easily.
Step 1: Add docker context to run docker-compose.yaml in ACI

Refer to this link for more information on setting docker context.
To repro your issue, I have executed docker-compose.yaml file with below configuration as like yours.

I got the below error after running the above code.

Now, I have modified the above code as below.

version: '3.9'
services:
client:
image: nginx
ports:
- '80:80'
volumes:
- nginxconf:/usr/share/nginx/html
volumes:
nginxconf:
driver: azure_file
driver_opts:
share_name: fileshare4dc
storage_account_name: strg4dc
storage_account_key: "xxxxxxxxxxxxxxxxxxxxxxxxx"
Note: ACI does not support port mapping as of now. Container port and ACI port must be same.
Now run docker compose and verify the container instance created.
$docker compose --project-name nginx-aci up -d


Compare the files in azure file share and ACI to check bind volume is working properly or not.
Below are the files in my Azure fileshare.

Below are the files in my Container.

Commands used in above screenshot.
$docker ps
$docker exec -it <container-name> bash
Whatever changes or files adding in Azure file share, it will reflect same in container.