I typically open tabs on android as I read, then want to spend more time with the content on the PC as a more comfortable space for reading.
I have the same problem with tabs as you mention with android not syncing to pc, apart from the current tab - but works from PC to android. I have tried signing out and back in of one, the other and both but this does not resolve. (I have also noticed that the person icon does not appear).
Thanks for any further advice on how to get it to work or any insights on whether this is a general fail...