After several weeks of daily use, I had this issue for the first time today. The only thing that has changed recently is that yesterday I started using an external 4k monitor as the primary display while using the laptop screen as a secondary display. Prior to this, I was using a lower-resolution external display in clamshell mode (the lid was closed so it was the only display).
What is strange is that, when trying to find ways to deactivate the screensaver without putting the computer to sleep, I activated Siri using the Touch Bar and asked her to "deactivate the screensaver". Instead, she "activated" a second screen saver over the first one. Moving the mouse made the second screensaver go away and reveal the first one again.