Update and reinstalling Mac OS hangs(MBA A1)

The first order of business would be to boot to target disk mode and make a backup of any key files or see if safe mode let’s you connect a USB drive.

• https://support.apple.com/en-us/HT201262

If that fails, I might call Apple for triage assistance. They would know if and when the 11.5.1 full installer is released and try again perhaps?

If multiple reinstalls all hang, the erase install is the next option short of getting someone skilled at reading the boot logs or install logs (to see what step hangs) as alternatives to entering hardware repair.

• https://support.apple.com/kb/HT208496