PeteSeta

Yes. Just reinstalling macos shouldn't erase anything, but you should backup your files anyway. There is also always the possibility of a virus, which the reinstall might not erase. It might also not solve the missing folder icon anyways because it's not a clean install. If you have a backup, will do a backup, or willing to risk some of your files, I would maybe try it. So your MacBook does boot to recovery right?

Glad to be of help. Please read the rest of the edited reply before this one. Here is what to do if disk utility cannot repair the disk and you want to attempt to fix it: You should back up any important data on your startup disk before erasing it. Erasing your startup disk deletes everything stored on it, including items in your home folder like your documents and items on your desktop. If you don't have a recent backup of personal data that's stored on your startup disk, you can use these steps to try to back up your data to an external drive: Connect an external USB, Thunderbolt, or FireWire drive to your Mac. The drive needs to be the same size or larger than your current startup disk. It also needs to be a drive that you can erase. Use macOS Recovery to erase the external drive, then install macOS onto the external drive. Make sure that you select the external disk as the one you want to erase. Don't select your built-in startup disk, usually named Macintosh HD. After installation is finished, your Mac automatically restarts from the external drive. When Setup Assistant appears, select the option to migrate your data from another disk. Choose your built-in startup disk as the source to migrate your data from. When migration is done, complete the steps of the setup assistant. After the desktop appears, confirm that your data is present on the external drive. Now that you've made a backup to an external drive, follow these steps: Use macOS Recovery to erase your built-in startup disk and reinstall macOS. Select the built-in startup disk as the one you want to erase, not the external drive. When installation is finished, your Mac automatically restarts from your built-in startup disk. After you erase your startup disk and reinstall macOS, your Mac automatically restarts and setup assistant appears. To copy your personal data back to your startup disk, select the option in the setup assistant to migrate your data from an existing Time Machine backup or other disk. Choose the external drive as the source to migrate your data from. If you're unable to erase your startup disk or reinstall macOS, your Mac might need repair. Make an appointment with an Apple Genius or an Apple Authorized Service Provider for more help.

Just to clarifly, did you try: Turning off your Mac by pressing and holding the power button for a few seconds. Press the power button once to turn your Mac back on. Immediately press and hold the Command and R keys on your keyboard to start your Mac from macOS Recovery. Keep these two keys held down until you see an Apple logo or a globe. If prompted, select a Wi-Fi network to connect to the Internet as part of startup. After the macOS Utilities window appears, choose Startup Disk from the Apple menu. Select your startup disk, then click Restart. If you don't see your startup disk in step 5, follow these steps: Open Disk Utility from the macOS Utilities window. In the Disk Utility window, select your startup disk (usually named "Macintosh HD") from the left side of the window. Click the First Aid tab. Click the Repair Disk button to verify and repair any issues with your startup disk. After your disk is successfully repaired, quit Disk Utility. Choose Startup Disk from the Apple menu. Select your startup disk, then click Restart. If you still don't see your Startup Disk, try reinstalling macOS on your startup disk. Also, is your model a Core i5 or Core i7?

It seems like critical system files are missing or corrupt. I would recommend you bring it to a repair facility and have them take a look at the drive. Does it look like this? Did you lose power during the update? Can you provide system details (What model specifically, how old, system version if you have a record) btw, did you say you saw this screen twice?