rvp I understand better now. Thank you.
After switching the boot console (by enabling /dev/ttyE0 and disabling /dev/constty in /etc/ttys), I’m starting screenblank from /etc/rc.conf with:
screenblank=YES
screenblank_flags="-d 300"
It works, but this leads to another issue:
screenblank only monitors input on /dev/ttyE0. The actual screen blanking, however, applies to all virtual consoles (ttyE1, ttyE2, etc.). As a result, when I’m actively working on ttyE1 (logged in as the same user), the screen still turns off. To wake it up, I have to switch back to ttyE0 and press a key.
I also tried launching screenblank as a different user (both from that user’s ~/.profile and directly from the command line), explicitly specifying the console device with -f /dev/ttyE1. The result is the same: screenblank only monitors input on the console it was started on and completely ignores keyboard activity on the other virtual consoles.