I can't find the /system/media/ folder in any root browser or TWRP File Manager

You should read the detail text of the Boot Animations for Superuser app. There you can find the following info:

Q: Is my device supported? A: Your device must be rooted to install a
boot animation. Some manufacturers, like Samsung, use a different boot
animation format (QMG) which is not compatible with this app.

Therefore the app does not work for Samsung devices. You need an app that is specialized to Samsung devices or that supports the QMG format.

And keep in mind the next section:

Q: The boot animation doesn’t play. How can I fix this? A: Some
Android devices use different install locations. You should find your
current boot animation location and change it in the app’s
preferences.

This explains why /system/media/ does not exist. Again Samsung seems to follows a different path that most of the other Android devices.