It’s not meant to be syncing. In fact, if you install the plugin, it won’t show you the lastly opened files, it just starts working after you installed it.
Maybe a Dataview query will work properly (check the forum) for this use case.
ah, I see I posted this a several months ago. Forgot about that. In my regular working in Obsidian on two devices I keep bumping against the lack of real time syncing of files I’m currently working in. I think it would be a workflow enhancement for many?