If the Companion is not connecting, the toolbar icon is red and the popup shows an open-Calder sign-in hint instead of the connected state.
First, sign in to Calder staging in the same browser where the Companion is installed. The Companion only accepts Mission context from approved Calder origins, so starting a Mission from any other site will not connect it.
Second, open a Mission from the Calder page. The Mission page sends the active Mission session to the Companion, and the popup changes from Checking Calder to Calder connected and shows the active Mission.
If you closed or reloaded the original Calder tab, the Companion loses its report path back to Calder. Reopen the Mission details page and start the Mission again.
If you use Firefox with a temporary add-on, remember it is removed when Firefox restarts, so reinstall it from about:debugging before testing again.
Still stuck? Remove and reinstall the unpacked extension, then open a fresh Mission. If the popup still cannot connect, the Mission details page also offers a plain LinkedIn link and a Mark complete button so you can finish without the Companion.