Why is "System" taking over 100 gigs of storage on my Mac?
System is everything on the disk that takes up space and does not fall under other named categories. Unless you have a spotlight issue or the system is still indexing, I would use a tool like Daisy Disk to get a second opinion on system.  Have seen it where a category doesn’t finish indexing so perhaps you have 80 GB of documents, but the indexer crashed at 80 MB and system looks bloated when it’s not.
While that’s running, be sure to take advantage of all the Apple steps to clean things you don’t need: https://support.apple.com/en-us/HT206996
If system remains larger than you like, back up and do an erase install. When you log in, you convince yourself the system is not bloated, but the things you've brought to the Mac are what use the disk space. After that, migrate your data or import things again.
To save a double erase, here are sizes of a survey of system sizing per system after importing apps and setting up users and using them for a week to a month:

Mojave: 23.17 GB
Catalina: 11.31 GB
Big Sur: 14.95 GB (M1 with Rosetta)

After an erase install, you should be even slimmer on the system sizes than listed above.