Using URL rewrite feature, you can translate URLs, query string parameters as well as modify request and response headers. https://docs.microsoft.com/en-us/azure/application-gateway/rewrite-http-headers-url
whereas Path Based routing is based on specific URL's to a specific backend. https://docs.microsoft.com/en-us/azure/application-gateway/url-route-overview
So no you do not need URL rewrite setting with Path based routing
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