Samsung started updating its phones with the June security patch before May was out, but the S21 series seemed to be having issues. Now things seem to be back to normal as the update is rolling out widely.
Google has posted images for the March Pixel update to the usual spots for manual installation, if you're too impatient to see it roll out via the traditional means. However, although this month's update is supposed to correspond to the latest Pixel Feature Drop, some of the new features don't seem to be live in the March update just yet. As we noted in our prior coverage, some things may require app updates or server-side changes before they work. (Update: Though they're almost all live for me as of around two hours later.)
By all accounts, Essential doesn't have a whole lot going on right now. It launched one phone about 18 months ago and has been cutting staff ever since. If Essential is working on another phone, it hasn't seen fit to talk about that. So, what is there to do other than keep the Essential Phone updated? Another month, another instant update for Essential Phone owners.