Are the recent Wolfenstein and Doom reboots set in the same universe

I've just played Wolfenstein II: The New Colossus, and noticed a number of strangely familiar elements from Doom (2016). Which makes me wonder, is the Doom reboot universe actually the Wolfenstein reboot universe 200 years in the future?

Below are some of the elements I've noticed so far:

1) Ubergewehr VS BFG:
The Ubergewehr, the most powerful gun in Colossus, has a similar missile explosion as the BFG in Doom. Not to mention the intel which states that the Ubergewehr draws energy from a third unidentified microportal source [Argent Energy?]. [I believe this has already been largely commented on by many netizens].

2) Samuel Hayden VS Ubersoldat and Da'at Yichud Head Transplantation Technology:
In Doom, we are told that Samuel Hayden, the UAC head, had his brain transplanted onto his present robotic body after suffering from a terminal illness. Hayden's robot body looks rather similar to the Ubersoldat androids seen in Colossus, with its tall and slender frame and skull-like head shape. Could they be historically related? Also, what if the technology that enabled Hayden's brain transplant has its origins in Set Roth's head transplantation technology as seen in Colossus?

3) Laserhund VS Hell Razer:
In Doom, we are told that the demons acquired human laser technology thanks to traitors like Olivia Pierce. I couldn't help but notice that the way Doom's Hell Razer fires its laser beam looks just like that of the Laserhund in Colossus! The suggested implications need not be stated…

4) Accelerated Energy Consumption VS Future Energy Crisis [somewhat speculative]:
In Doom, Man's tapping of Argent Energy was meant to solve an energy crisis on Earth. Now, seeing that the advanced Nazi technologies in Colossus (stolen from Da'at Yichud) appear to consume obscenely large amounts of energy (electricity to power the laser charging stations, diesel for vehicles and diesel-based weapons etc), could such an accelerated depletion of Earth's energy resources in the Nazi-occupied world of the late 20th century (as compared to our real-life timeline) have led to the burgeoning energy crisis faced in the 22nd century (Doom)?

Feel free to share your suggestions or any other things you guys may have noticed. Cheers!