So, I opened Native Access and most of the libraries had a "repair" warning button next to them.
I checked the "Installation paths" on a couple and noticed that they were missing a part of the path for whatever reason. I configured the Content Location to be at my external SSD way back, before installing the plugins/libraries/what have you.
The "Installation paths" were missing the "/Volumes/" first part of the path. I have no idea how this happened, but well, it did.
So I quit Native Access, backed up "/Users/Shared/Native Instruments/installed_products" and then ran:
find "/Users/Shared/Native Instruments/installed_products" -type f -name "*.json" -exec sed -i '' 's|"/EXTSSD/NI/|"/Volumes/ETXSSD/NI/|g' {} +
where "EXTSSD" is the name of the drive under which it is mounted in /Volumes.
Then launched Native Access and voila, everything is fine now and libraries/plugins are in state "Installed". Whew. Was not looking forward to reinstalling over 300GB worth of stuff, don't need to.