MacOS Update "Storage Required" Bug

Have you tried starting up in Safe Mode, the maintenance tasks may free up some redundant space.

If you have Time Machine enabled you can force it to delete Local Snapshots by turning TM off, waiting until it’s deleted the local snapshots and then turning TM back on.

This may not help, but it is good practice before updates/upgrades are started, to uninstall any redundant apps (especially anti-virus / cleanup apps), shutdown any running apps, turn VPN off.

Agree with previous posting above.

Question - is the installer being pointed to the small Internal Drive or to the External Drive as represented in the last image of yours

To get a more True Representation of the Internal Drive usages - Rebuild the Spotlight index on your Mac

What is “Other” storage on a Mac, and how can I clean it out?

Free up storage space on your Mac

OmniDiskSweeper Safe to use

GrandPerspective 

How to delete Time Machine snapshots on your Mac

See used and available storage space on your Mac

Locate backups of your iPhone, iPad, and iPod touch

The final word from Apple on Managing the " Other/ System Data “ Category

Other / System Data: Contains files that don’t fall into the categories listed here. This category primarily includes files and data used by the system, such as log files, caches, VM files, and other runtime system resources. Also included are temporary files, fonts, app support files, and plug-ins. You can't manage the contents of this category. The contents are managed by macOS, and the category varies in size depending on the current state of your Mac.

since you are running low on space, you can purchase an external HDD or SSD of sufficient capacity and move your larger files (videos, pictures, documents, etc...) to it. once they are on the EHD, you can simply erase the same files from your internal drive. and, if it's just going to be used for storage, you can use an HDD and save a few bucks over the cost of an SSD. FWIW, i personally keep very little on my internal drive.

Lucas.Godfrey wrote:

I’ll go ahead and rebuild in a bit, I honestly didn’t know you could direct the update to an external drive. Do you think that’s something I should try?

Is that what you want ?

If not - No.

Would suggest removing the External dive during the upgrade process - it is IMHO better to have a clean and unencumbered computer wit External Drives attach especially during a major upgrade as Monterey 12.5

The alert dialog is correct. You are out of free disk space. That “Storage” hasn’t told the truth since it was introduced. It only reports some level of “available” storage that is simply a fantasy.