As an individual user and a developer, I expect my click's effect to occur at the closest possible area to the button/item. Since the main idea behind the action should be realizable by the observer (otherwise it wouldn't count an experience if the user can't follow the rest of the events fired), it's preferable to keep the action(s) user's insight.
So even it is a learned behavior or basic instinct, it should be naturally visible to the user interacted with it to be taken into consideration.
As we think about the layout from the start of the project, probably the adaptivity for mobile would be the critical point to taken into account. While there are practices for mobile like Reachability, Rule of Thumb and way more academic & scientific searches, the menus/menu icons are practically used at either top corners or as a buttom navigation as argued with the prior questions asked like this and that.
Even I do not have any direct research(es) specifically focused on your exact questions, with the overall assumptions from what I have read (articles/researches of consulters, Nielsen Norman's Group, heatmap analysis and some trends blog, etc.) is, I thought or I ran into the examples with the actions on the same spot with the icon/button/text.
Even I can't see the default placement of facebook's newsfeed menu from the visual you provided (and even I couldn't locate myself), the second image seems utilizes the menu icon on the central left and places the hamburger menu's content like a right side navigation as an unusual practice.
I thought I can share my own journey as an experience at least since I can't locate any research about this specific topic after your edit.
The idea is quite tempting for me and even might be a better alternative for the group of more suitable users where creativity and differantiation from mainstream experiences targeted. But the custom effect as I experienced with the most of the web/app is the same side buttons & drawers.
By the examples you provided I suppose, they seem like to consider using the extra space on the right side since they're desktop websites and have a content on the left to interact. Besides, there might be a case of compulsory situation by the author to save space or not to hide the visuals on the left pane (A good use case for commercial purposes).
PS: As the "user experience" optimizes the researches on different cases with different demographics with it's effects, it should be healthier to watch the analytic results at all for the all cases.