Hi,
I assume you are using Azure Database for PostgreSQL Flexible server. Please correct me if my assumption is wrong, and specify precise service you are using.
You may monitor connections using Metrics blade -- Add metric -- Traffic - active_connections or by querying pg_stat_activity. You may need to switch to higher SKU using Compute + storage blade.
Which SKU are you using? Each one has a maximum limit, which you may be hitting, especially if you are using B1ms SKU. Some of the SKUs with their limits are shown below:
Limits in Azure Database for PostgreSQL - Flexible Server
https://learn.microsoft.com/en-us/azure/postgresql/flexible-server/concepts-limits
Please click Accept Answer and upvote if the above was helpful.
Thanks.
-TP