We can't manage at this moment the usage of the PDF Markup service in Web connections. When the service is deployed on the WSG server, it's used automatically when we click a PDF or an Office document in PW Web. It's not what the users want and we need to manage the usage of PDF markup by application, by document.
A management by application should be done through ProjectWise Administrator and applications settings with the Associated Web Viewer setting in Association tab : 'Windows IE association' to rename in 'Default Web browser association' would not use PDF markup service even if deployed but the default web browser association (PDF web default connector, Office 365 when installed on user PC, etc... And add a 'PDF Markup service' to use the service when deployed and appropriate for the application. See the screenshot attached for this suggestion.
A management by document would be great by adding in Web connection a 'PDF markup' action on a document in the Web like it exists in PW Explorer. It will allow to force the usage of PDF markup if the default application web association is the default web browser association. It will give also more consistency between the 2 interfaces. This request is asked by multiple users because they prefer generally the default web association when they just want to view a document instead of PDF markup.