To boot into System with Magisk root you HAVE to use key combination for Recovery, then, when the device vibrates with a splash screen, release all buttons EVERY TIME you boot device.
Nb. Unless you boot that way, root (if present) was actually installed as Magisk in Boot. PW
I recognize what you say as the way it was described in Magisk/install.md when I was trying to install Magisk. I don't know if Magisk was changed between the time those notes were written and the version I installed, or if there's something special about some devices, but I routinely shut down and reboot and Magisk is active.
I'm sure Magisk is installed in recovery, because I had to struggle to boot almost-but-not-quite to recovery when I first installed. After repeatedly booting to no Magisk, I finally got the timing right and got "Magisk needs to do more setup."
What I have read in posts is that it's using the Reboot option on the Power button menu that boots without Magisk -- after doing that, you need the horrible almost-recovery boot sequence to regain Magisk.
TL;DR On at least some devices, with Magisk installed in recovery, complete shut down followed by power-on reboot will not lose Magisk active.