Liz,
You can use vSphere web services to get the list of extensions. This can be done by querying the "extensionList" property of the "ExtensionManager" object
http://pubs.vmware.com/vsphere-51/index.jsp#com.vmware.wssdk.apiref.doc/vim.ExtensionManager.html
If you want to get that from within your web client plugin, then I suggest take a look at the sample that illustrates using the vsphere web services from within the web client. You can modify that to query the above property.
~ Sidharth