I would like to know if adding a new web and configuring backend pools, backend settings, listeners, and rules in the production environment will affect other online systems or not.

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There should be no disruption if the Connection Draining feature is enabled on your application gateway.

Azure Application Gateway supports a connection draining feature, which can be enabled via HTTP settings. You can set up connection draining to change members within a backend pool without disruption.

Connection draining helps you achieve graceful removal of backend pool members during planned service updates. Once enabled, the application gateway ensures all deregistering instances of a backend pool don't receive any new requests while allowing existing requests to complete within a configured time limit. It applies to cases where backend instances are explicitly removed from the backend pool after a user-initiated configuration change. Connection draining is invoked for every single update to the gateway.

The only exception is when requests continue to be proxied to the deregistering instances because of gateway-managed session affinity.

It is highly recommended to make changes to the Application gateway during a maintenance window to avoid any unforeseen issues/events.

Additional reference: https://learn.microsoft.com/en-us/azure/application-gateway/application-gateway-faq#does-application-gateway-support-connection-draining

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