Accidentally shutdown my MacBook Air during a software update, now it displays odd messages and won’t turn back on, help!

I change the order of actions. Works for me although apple documents your way.

• Hold the power button down until the device turns off
• Hold the SHIFT button down
• Press the power button again to turn it on
• continue holding down until you see something on the screen.

I doubt safe mode will work, but you never know until you try.

Either your filesystem has problems or your drive is going bad. I'd try again to get into safe mode. Safe mode checks and repairs the filesystem.
Try a safe boot.
Shutdown your machine. Hold down the shift key. Poweron. The boot up will take longer than normal because the filesystem on the startup drive is being checked and repaired as needed. All about safe mode including what features and apps safe boot leaves out.
http://support.apple.com/kb/ht1455

How old is your mac? Harddrives start goin' bad at three to five years. You could get an external drive and install macOS on it.

Do you have backup? if no, and you need to recover your data. See this link:
backing up from the command line via single user mode.
https://discussions.apple.com/thread/8101803?answerId=32357328022#32357328022

Or, you need to pull the drive out and place in external drive enclosure to recover the data.

Your post has the machine stopping in the middle of a boot.

-1- Safe boot may work. power off. hold down option key. power on. wait to see icon.
-2- single user mode may work power off. hold down command + s key. power on. wait to see icon.
-3- command + r should work. power off. hold down command + r key. power on. wait to see icon.
-4- option + command + r should work. power off. hold down option + command + r key. power on. wait to see icon.

try in this order report the results for each.

How to re-install MacOS
https://support.apple.com/en-us/HT204904

Boot to Startup Manager

Power off your machine. Hold down the option/alt key. Power on your machine. Continue holding down the option/alt key until you see an icon. Click on the start drive you wish to boot. Click on the right arrow icon or press the return key.

https://support.apple.com/en-us/HT202796

What kind of odd message? I recommend you try the following:

• Hold the power button down until the device turns off
• Press the power button again to turn it on
• As the device powers on, hold the SHIFT button down

If that doesn't help, follow the three steps above but instead of holding the SHIFT button hold the R button and the

 (command)button down at the same time.