Question regarding 'boot wait for network' setting in raspberry pi

Hi, so I had some issue with my raspberry pi randomly shutting down, after some suggestions I had changed my power supply and it seemed that it fixed the issue. I’m was still confident that the issue got fixed, however today something happened and it seems that the raspberry pi shut down / lost power from load shedding and didn’t come back online.

The problem is I am not on the premises of this raspberry pi so I am not sure what caused it to lose power, In fact I’m a few continents away. I’m trying to find out why this went offline, that’s when I realised that the router sometimes takes a while to boot up. I also noticed that there is a ‘boot wait for network setting’.

Would disabling this setting help the raspberry pi with a situation where the router fails to boot up? The reason I’m asking this is because when I’ve asked people on the premises to reboot the raspberry pi by disconnecting power and replugging it in, sometimes it still doesn’t respond to my pings (as if it’s stuck booting) and I’ll have them reboot it two or three times for it to start responding.

Could someone please give me insight as to what could be happening and if changing this setting would not mess up anything?