Good place to start even if not sure where to place this question.
Firstly, Attempting to Install Monterey on an External Drive is very problematic at Best. That does not mean it is impossible but very iffy.
Secondly - Partitioning an External Drive to be used for Two Very efferent purposes - Bootable Drive and TM Backup is not so good.
Reason, all the Eggs in One Bucket and the Basket fails - Scrambled Eggs
Thirdly and most important in this computers' setup.
There are reports appearing on the ASC Forums regarding failed installation of Monterey on older Qualifying Apple Computers. In most cases this is related to having a NON Apple Original Internal Drive ?
The EFI Boot ROM included in Monterey is verifying for Original Apple Drive and if not found , may Balk or fail to upgrade to Monterey.
Reports indicate the EFI BOOT ROM is Required to Flash the Computer and is a requirement for a Successful Monterey Installation.
Fourthly - Even if you were able to clear Enough Space on the 128 GB Drive , it is going to be a challenge to keep at least 15% to 20% of the Drive Total Capacity as Empty Space for good operations of the computer and for additional updates to Monterey to download, expand and install.
What is “Other” storage on a Mac, and how can I clean it out?
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OmniDiskSweeper Safe to use
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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.
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