Unable to update???

I am trying to download and install the latest incremental update after OS 11.5.2. I have a 2019 MacBook Pro with an Intel I-7 chip. I'm having the same problem that I've been having with every OS update, minor or major, for a year at least. It downloads, and then when it gets to the point where it says, "Preparing Mac OS Big Sur 11.6..." and it shows "About 10 minutes remaining" the process seems to stop. It never goes farther. The little red circle with the "1" that is in the upper-right corner of the System Preferences icon at the bottom of the screen never goes away, which leads me to believe that the update was not completed.

About a year ago, when I first encountered this problem, I searched these Support Communities and found a thread where people shared that they were having the same problem but were able to download and install the app by booting in Safe Mode. I tried it and it worked for me, so that is what I have been doing for all OS upgrades since then. This time, it seems like it is not working, but I can't be sure. One of the reasons is that I can't tell whether I am in Safe Mode. I have tried shutting down and re-booting and following the instructions to boot in Safe Mode but the opening sound is not occurring, so I am not sure whether I'm hitting the space bar soon enough. I also can't remember what the screen is supposed to look like when in safe mode vs regular mode. Isn't there something on this machine that will say "Safe Mode" if it's booted in Safe Mode? I have tried to research this on the internet, and found an article about it, but it didn't say how I could find the menu where the boot mode is listed.

Any help would be much appreciated! What I would especially appreciate would be any advice that would make it unnecessary to go through this business of booting in Safe Mode just to update the OS.