I mentioned that I have not been able to locate a screensaver. I guess that does not really matter anymore because I found something else. I was searching my Pixel's settings when I found a BATTERY button. When I clicked it ChromeOS was kind enough to tell me how much power each application was consuming. And not not my surprise... mail.google.com and play.google.com, combined, were consuming about 70% or my energy needs.
I cannot do much about that other than to plan better by using my phablet when it counts.
** This seems to be an opportunity for Google to optimize gmail's power consumption for both smartphone and laptops.