Newly created music library access issue, new to plex and need pointers please

Your logs are showing it is processing loudness for music files

Sep 13, 2024 14:51:30.189 [139917934263096] DEBUG - Looking for path match for [/volume1/music/Free/1973 - Heartbreaker (Remastered 2002)/12 - heartbreaker (rehersal version).mp3]
Sep 13, 2024 14:51:30.212 [139917934263096] DEBUG - Skipping hash check, no size match for 8249555 bytes.
Sep 13, 2024 14:51:30.212 [139917934263096] DEBUG - No match for hash.
Sep 13, 2024 14:51:30.285 [139917934263096] DEBUG - Added new metadata item (Heartbreaker) with ID 38930
Sep 13, 2024 14:51:30.286 [139917943978808] DEBUG - [LibraryTimeline] Scanner activity on section 2: 20195 added, 28 deleted
Sep 13, 2024 14:51:30.366 [139917934263096] DEBUG - Looking for path match for [/volume1/music/Free/1973 - Heartbreaker (Remastered 2002)/14 - easy on my soul (rehersal version).mp3]
Sep 13, 2024 14:51:30.396 [139917934263096] DEBUG - Skipping hash check, no size match for 12498946 bytes.

I would advise a few things at this point.

  1. Let the music finish ingesting.
  2. Review to make certain it all matched. (Your naming is not per Plex naming rules – See below)
  3. Make certain you have allocated & room for more

You really need Plex standard naming and structure for best experience.
I bit the bullet and now, with my automation in place, everything incoming is always perfect and nothing ever missed.

https://support.plex.tv/articles/naming-and-organizing-your-tv-show-files/

https://support.plex.tv/articles/naming-and-organizing-your-movie-media-files/

https://support.plex.tv/articles/200265296-adding-music-media-from-folders/

There’s a lot of info in the support pages. Good examples too.
Plex is generous about naming but a few basics are needed/required.

You can search for movies, series, photos, etc
https://support.plex.tv/articles/?s=naming+music&search=support_articles

And then, to augment your syno:

specifically: