(An earlier version of this post was too confusing so I redacted it.)
I went ahead and tested this and the answer is: No, observers have no share button, so they obviously can't share--makes sense.
However!
There seems to be no clear cut documentation about this, and if there is, I'd like to know where that's at.
Additionally, the support bots were contradicting each other. One said:
Currently, Trello does not offer [...] permission to allow guests/observers to be added to boards but prevent them from inviting others.
So that's a) wrong (?) and b) confounding guests and observers. It's not clear to me at least.
Adding to all this, is this setting:
"Sharing boards with guests: Anybody can send or receive invitations to boards in this Workspace"
Is "anybody" anybody in the Workspace, anybody who's a guest? What about board admins only? If observers indeed cannot do that, it's not 'anybody'.
So I made a confusion more confusing but here we are.
