Ever increasing disk space needed for installing Monterey

There is free space and there is "available" space. To install Monterey you need about 45GB of free space.

Anyway, it is not a good idea to work, let alone, upgrade your mac, with very low space.

You are not telling us how big your drive is, or how much that space is free or just "available".

To better advise, we need more information.

1) Select your drive in the Finder, and press Command-I to open the Info window. Post a screenshot.

2) In Terminal, paste the following command and tell us what output you get:

tmutil listlocalsnapshots /

3) Please run Etrecheck and post its full report here. Use the "additional text" button and paste the report into the text box.

There is " Free Space " and then there is " Purgeable Space "

Free Space is available to the Operating System immediately

Purgeable Space is managed by the Operating System and not the user

When the Operating System deems it necessary, it will release some of the Purgeable Space back to the Operating system as Free Space

This transfer from Purgeable to Empty space can take some time and can take a day or more

There is nothing the User can do to hasten this process.

t is generally a good computer practice to alway keep at least 15% to 20% of the Total Drive Capacity’s as Empty Space. Allowing the computer to drop below these guidelines may eventually, cause unintended consequences.

The links below will assist in identifying what is taking up space on the Internal Drive and provide possible ways to remove data that is under the direct control of the User ( Home Folder ) . 

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. ⬅️

Notation - If the user is using a cloning software like Carbon Copy Cloner - suggest tweaking the Safety Net Feature in this software. It may be making additional Snap Shots that are not being Cloned to the Eternal Drive. If this should be the case, these Snap Shot could be using additional space on the drive 

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.

EDITED

Should the Etrecheck report prove fruitful - any credit for this suggestion would belong to @Luis Sequeira1