Primarily the first paragraph.
The issue is that the entire main site now uses a system that makes things like relying on Tampermonkey to be notified when the current URL changes at best unreliable (i.e., it will fail on any situation other than a complete page refresh or the first time the tab is opened). Things like navigating between pages now no longer trigger a script to run, unless the new system is accounted for.
Basically, if you’re not hooking into Turbo events in your script, your users will have issues, period.
Whether you choose to use this library for it or choose to do it yourself is up to you, however.
There are also some other libraries, such as WaniKani Item Info Injector, that have incorporated their own system for dealing with the Turbo events into their logic, so some scripts that already relied on those were able to get by without updating them if people have the newer version of the library installed locally.