Okay, I had this same; if not very similar problem; myself. I tried turning off my watch and restarting, I tried turning off my iPhone and restarting. And I tried some other things and none worked until I did what I am about to describe below, step by step which seemed to heal me. First off, I have an iPhone 6 Plus and I have two apple watches: a series 2 and a series 3 with cellular. I had the song updating issue on both of my watches, not just one of them. And, to be clear, my updating issue was that the songs took a very long time to update to my watch(es). When there was any progress at all, it would be about one song per 20 minutes or more. It finally got to the point that no songs would even update to the watch: I would instead see a message like: updating song 120 of 175. And that message would be there for hours and hours with no progress. If this is your issue, please see what I did below. I could guess as to what the root cause was, but I won't do that. I will just tell you what I did that seemed to heal me. I hope it heals you too. I don't know if every single step is critical but it wouldn't hurt to do everything I did (because I didn't do anything too crazy like resetting the watch or removing a watch setup from the phone). And while I have two watches, I did the following steps, one by one for each watch...so, for my two watches, I went through the steps twice (once per watch).
Here, then, is what I did:
1. On your iPhone, turn Bluetooth OFF. (Bluetooth is how you phone and your watch communicate.)
2. On your iPhone, go to the WIFI settings. Then "FORGET" the WIFI network that you are currently connected.
3. At this point your Bluetooth should still be OFF. And NO network should be connected to your phone. If you have WIFI networks automatically connecting to your iPhone (shame on you) you need to stop those. The objective is to NOT turn WIFI off but to keep WIFI on but have NO WIFI networks connected to your phone.
4. Again, don't continue until you have ensured no WIFI networks are connected to your phone while your WIFI toggle is still on (green)
5. Now, and this may seem odd but please do it, reconnect to WIFI. Don't connect to a 5GHz network--this is not compatible with apple watches. My wireless router transmits both a non 5GHz signal and a 5Ghz signal, yours may as well. It is important that you connect to the non 5GHz WIFI signal (presumably the 2.4GHz signal).
6. At this point, on you iPhone: Bluetooth is STILL off (Step 1 of this instruction sheet) and WIFI is connected to the WIFI network you just selected.
7. Now check out your watch (these steps work best if the watch is on your wrist and you have unlocked it). Verify your watch is NOT connected to your iPhone. You should see a red X at the top of the watch or NOT CONNECTED in red font or something similar to indicate that your watch is not connected to you iPhone.
8. On the iPhone, turn Bluetooth ON. (This will re-establish an iPhone to watch connection.)
9. Check out you watch. You should now be connected to your iPhone. Your red X or disconnected message should be gone.
10. On the iPhone, now, turn Bluetooth OFF and turn WIFI OFF. That's right, turn them BOTH OFF on your iPhone.
11. Now, it may take several seconds, but your watch is going to do something pretty cool and perhaps you may have never realized it could do such a thing: it is going to be connected to your WIFI directly without leveraging your phone. But before we get ahead of ourselves we need to make sure that the iPhone to watch connection is truly disabled. For me, I had to do some unexpected things because the watch really wants to stay tethered to your phone. To make sure you really get iPhone talking to a WIFI without leveraging your iPhone, do step 12 (the next step now).
12. I didn't think this was necessary and perhaps I was just being impatient but I finally turned airplane mode ON on the watch. After 15 or 20 seconds, I turned airplane mode back to OFF on the watch. At this point, verify that on your iPhone that airplane mode is OFF (my airplane mode went ON on my iPhone when I turned airplane mode ON on my watch). So verify that airplane mode is OFF on your iPhone and that Bluetooth and WIFI are still OFF on your iPhone.
13. Okay, at this point your watch is doing something very powerful, it should be connected to WIFI completely independently of your watch. To prove it, raise your wrist (or however you activate Siri on your watch) and ask Siri about the weather outside: "Hey Siri, is it going to rain outside?" Siri should answer you. If Siri answers you, you have validated that your watch is no longer connected to your watch and is connected to WIFI directly. Ask Siri another question like: "Hey Siri, what time is sunset (or sunrise) today?" Again Siri should answer.
14. For me, I think forcing Siri to get on my good 2.4GHz WIFI signal was the key to fixing this whole issue. I could be wrong but that is my opinion. (So step 14 is just my editorial, no real steps to execute).
15. Now, go back to your iPhone. On you iPhone, turn Bluetooth ON and turn WIFI ON.
16. Take your watch off and attach it to your apple watch charger.
17. On your iPhone, go to the watch app and select Music to see if music is now updating to your watch. Be patient, it does take several seconds (maybe 30 to 90 seconds) for your iPhone and apple watch to engage and start the music updating process. The good news is that after that initial handshaking is completed, your songs should start flowing into your watch. For me, the songs starting importing into the watch at the rate of about one song per 20 seconds. Some songs took 30 seconds, some songs took 7 seconds. But songs definitely were moving SIGNIFICANTLY better than before.
18. On one of my watches (remember I had to do this for both of my watches) songs were still not moving onto my watch. Maybe I was just being impatient but nonetheless: I unlocked my watch while on the charger and navigated to the music icon. I clicked on the music icon and while scrolling through albums, I noticed that for the New Music Mix playlist and the Favorite Mix playlist and the Chill Mix playlist all had the "swirling circle" appearing in the lower right hand corner of the playlist covers which, to me, meant they were busy (or just plain confused) with those playlists. Therefore, I went back to my iPhone and and turned the slider OFF for the New Music Mix, Favorite Mix, and Chill Mix. I waited a 10 or 20 seconds and turned the slider back ON for those 3 playlists and the song progress started. And to push my luck, I added a favorite compilation album to make sure those songs (the entire album) was imported into my watch. I am happy to say, the album loaded those several songs, too, into my watch at the rate mentioned above.
THAT IS WHAT I DID. I HOPE IT WORKS FOR OTHERS THAT MAY A SIMILAR ISSUE. AGAIN, I SUPPOSE MY STEPS, OR AT LEAST SOME OF THEM MIGHT BE TECHNICALLY UNNECESSARY, BUT THIS IS WHAT WORKED FOR ME. GOOD LUCK TO ALL OF YOU. AND YES, I AM HAPPY AGAIN! I HOPE YOU WILL BE TOO.