Is there a safe way to softly shutdown iMac via start-button?

I use my iMac 2011 in Target Display Mode under High Sierra, to use it as an external display for my M1 MacBook Air from 2020. (works well, despite Apple websites say newer than 2019 is not supported). It has no keyboard, no mouse, and no internet connection - WIFI and BT turned off. On the iMac, I created a user that automagically logs in to MacOs. When I plug in DisplayPort cable to the laptop via a mDP 1.4 adapter, the Mac automatically switches into Target Display Mode. See picture for my DisplayPort adapter. What I would like is a way to shut down the iMac nicely, not a hard stop by holding the start button for N seconds. For example, on my Linux NUC, I can shut down smoothly by hitting the on/off button twice in a second. Can this be done on macOS (especially High Sierra) too?