“a critical software update is required for your Mac, but an error was encountered while install this update”
Apparently this is a common alert. I have it on a pre used MBP A1707 I bought. It was sat on so has physical damage but seems to work fine apart from the smashed trackpad glass (it still works) and backlight smudges on the screen. I'm running Ventura.
This you tube shows a 'temporary fix' that worked for me.
https://www.youtube.com/watch?v=9b6A_mJRjHU
Basically do this.
Startup holding down the shift key to enter safe mode.
Join your network
Open system preferences and click on your network "details"
Click TCP/IP button and find "Renew DHCP Lease". Click that to renew it.
Now restart.
Good luck. 🤞
MacBook Pro 15″, 13.6