When the work object is opened in new browser tab using snapstart url or worklink url, it opens the work object in review mode and dynamic container will not be available in that page.
All the case level actions like finish assignment, openworkbyhandle will open in separate window. The dynamic container is needed for harness switching like switching from review to perform for performing assignments and to open any links in the page using openworkbyhandle.
the newly opened tabs will create the synchronization issue if the snapstart/worklink threads shares the same name.
In case of theme cosmos application it has the ajax containers and the case processing can be performed on it.
To open the work object in new browser tab it is highly recommended to use Theme Cosmos OOTB way of opening the work object in new tab or use the copy sharable link feature.