Hard to upgrade to Big Sur with iCloud storage optimisation

Suggest having at least 50 GB of Empty Space on the drive.

It will allow the Full Version ( about 12.xx GB ) to download, expand and then commence to install.

It 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.

There is Purgeable Space and there is Empty Space.

Purgeable Space which is Controlled by the Operating System. When the Operating Systems decides the computer needs additional Empty Space, it will move a portion of the Purgeable to Empty space

AFAIK - there is no User Actions to hasten this transition from Purgeable to Empty Space

It can day or longer before this will occur  

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.  

Often caused if the Time Machine Drive has not been attached  to the computer and TM Backup is set to run on a Schedule. 

TM Backup will make Snap Shot on the Internal Drive awaiting the TM Backup Drive to be attached. 

Only then will the Snaps Shots be transferred to the External Drive and deleted the Internal Drive.

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 - and https://bombich.com/kb/ccc6/automated-maintenance-ccc-safetynet-folder 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.

By all means, proceed as has been outlined in your above.

Turn OFF iCloud and remove all that is stored on iCloud from the Internal Drive.

Have worked with several Users with the tiny 256 SSD - 500 GB Drives and a huge iCloud Capacity of 50 GB.

They have tried a similar methods as you have outlined above and it has worked

They came back complained iCloud took about 24 - 36 Hours before the Sync was completed.

In their cases - the issues were Running behind a VPN connection, running Third Party Security Software , having a slow 25 download / upload Internet Connection

Shortly after that, they we back again complaining the Computer would not upGraded to the next qualifying version of macOS

Kept getting the error message " Not Enough Empty Space " to upgrade.

This is one of the downsides of not keeping up-to-date.

There is an option to remove individual iCloud files. You can locate your largest files, control-click or right-click on them, and choose "Remove download". That will evict the file from iCloud and recover the space for that file.

Unfortunately, I don't know if that feature works on Catalina or not.