You are not supposed to use the selection in the Sequence Browser module (selection can change when new sequence is loaded or the user modifies the selection for any reason, etc).
If you expect to have only a single sequence browser in the scene then you can get it from the MRML scene using GetFirstNodeByClass().
If you have multiple sequence browser nodes then you can add a node selector widget in your module GUI. You can make the chosen sequence browser node selected in the toolbar using
If you want to mirror browser node selection of the toolbar then you can retrieve the toolbar from the sequence browser module and add a connection to its activeBrowserNodeChanged signal.
If all these still cannot satisfy your use case then we would need to learn a bit more about what would you like to do and how. We could add an accessor to the currently selected browser node in the toolbar or maybe save the currently selected browser node on the toolbar to the singleton Selection node.