If your Azure Database for PostgreSQL Flexible Server instance is experiencing connectivity issues and is stuck in a restarting state due to full storage, you can try increasing the storage capacity. If allowed and the option is not grayed out, you can do this by scaling up the storage capacity of the instance.
If the instance remains stuck in a restarting state, you may need to wait some time for it to come back online. When the storage is full, it can take a while for the instance to recover. However, if it continues to take an extended period, you'll need to open a support case, as backend intervention may be required to increase the storage and bring the server back online.
Thank You