The FOLDERS found by going to [UTILITY] > "Contents" > "Data Utility" show what is currently in the USER Bank (RAM) area of your instrument for Arps and Waveforms.
The ARPs shown in the Arp Folder at any time are only the ARPs that are currently in the USER BANK.
The WAVEFORMs shown the Waveform Folder are only the Waveforms that are currently in the USER BANK.

You cannot see if a Library has Arps and Waveforms by looking in the "Data Utility" Folders.

If you acquired a Library (purchased or downloaded) the first and best way to know if there are custom Arpeggios and/or custom Waveforms included with the Library is to READ the DOCUMENTATION that comes with the data. (No doubt).

If you wish to view the Arps that are included with a Library that you have already installed, you can follow the steps below to do so:
Recall an "Init Normal (AWM2)' Performance
From the Home screen: Touch "Motion Control" > "Arpeggio"
Here you can tap the first ARP assignment slot to see the pop-in menu - (as if you were going to search for Arp content)
Tap "Category Search"
The purple Category Search engine for Arpeggio data will appear.
Tap the "Bank/Favorite" box to see a list of your instrument's current data... you'll see "All", "Favorite", "Preset", "User", and each of your instrument's currently installed Libraries by Name... listed.
Move the highlight to focus on each Library, in turn, to recall the list of Arpeggios contained within, if any.

If you wish to view the Waveforms that are included with a Library that you have installed, you can follow the steps below to do so:
Recall an "Init Normal (AWM2)" Performance
From the Home screen: Touch PART 1 to *select* it
Tap EDIT
Along the bottom of the screen tap "Elem1" to view its parameters -- we are proceeding in a similar fashion as to how we would if we were going to select a new Waveform for this Element...
On the "Osc/Tune" screen tap the Waveform box at the top of the screen (currently on an Acoustic Piano (Preset) Waveform.
The amber Category Search engine for Waveform data will appear
Tap the "Bank/Favorite" box to see a list of your instrument's current data... you'll see "All", "Favorite", "Preset", "User", and each of your instrument's currently installed Libraries... listed
Move the highlight to focus on each Library, in turn, to recall the list of Waveforms contained within each.

Final Note:
Once you create and install a Library, its data is cataloged/listed and found in the same manner you would find Factory (Preset) data. And that is the point! A Library is created by taking certain User Bank data and writing it to a LIBRARY FILE.

A Library file is different from a User file - the contents are slightly different (a Library does not contain your current Utility settings, for example) and the FILE itself contains special instructions as to where to place the contents when you LOAD (install) a LIBRARY to ROM ("burn" into your instrument's internal memory). You certainly should not simply change the extension of a USER File. Doing so means you do not yet appreciate what is going on -- if you're a newbie, not to worry, but you cannot just change the extension and get the intended benefits.

Why is so complicated? It is because of the amount of data required to recreate the initial oscillation (tone) when the synth engine is sample-based.
Using Audio data to recreate oscillator Waveforms within a synthesizer is quite a bit different when compared to other methods of synthesis.... and is why managing it is no trivial matter. The sheer size of the data can be astronomic when compared to what it takes to create an entire FM-X synth sound.

Let's say your FM-X electric piano sound, complete, is around 2KB worth of data... compare that with the Chick Corea Mark V electric piano sound which is around 400MB worth of data, just to recreate the oscillator (the waveforms).

Perspective on the size differences of the data being handled: KB vs MB:
You get a call to play a gig next weekend - and they tell you it pay $2,000. Pretty cool.
You no sooner hang up, and you get another call, this other gig pays $400,000,000 - quite a difference, n'est pas?

-- or if dollars don't do it for you --

(2KB) 2,000 seconds is 33min and 20secs
while
(400MB) 400,000,000 seconds is 4,629 Days, 15 Hours, 6 Minutes and 39 Seconds

So the oscillator recreation in any sample based synth means you are typically managing data on a massive scale. It is why you want avoid having to WAIT for all that data to load each and every time you need it. Think of a LIBRARY as being installed... as opposed to just loaded. "INSTALLED" used here to emphasize that once installed it is designed to STAY PUT so that whenever you wish to access this data you simply have to recall it same as if it was installed at the Factory as a PRESET (This means you do not have to WAIT twenty minutes while it reloads each time you wish to use it). It stays in READ ONLY MEMORY. Advantage - it stays put.