iTunes (Music.app) not converting song entirely / skip to the next one when playing When using iTunes for AAC conversion, sometime only a part of the song is converted (also, when playing the song, iTunes does not plays it entirely and skip to the next one before the end).
But when I use another app (like MediaHuman Audio Converter for conversion or IINA for playing), the song is converted/played entirely.
The issue clearly comes from iTunes but I cannot find it. I looked up into the information of the songs having the issue in iTunes but the pre-ended box is not checked.
So far I tried to :

consolidate my library (from Apple support)

rebuild a new Library with the .xml file (following that procedure)

reboot into safe mode


but the problem still remains.
It appear that when testing with a new user account (with same file), iTunes manage to do it...
I never signed into my Apple ID, and my library is stored on my boot volume (~28,000 songs for 125 Go).
Anyone with a similar issue and/or knows how to solves it?
UPDATE :
It looks like the issue only occur when opening a full album into iTunes, and that the duration of each song will be equal to the shortest one (for example : if the shortest song is 2:36,  every other will skip at 2:36).
Sometimes it goes well for the first song of the album (even if it´s not the shortest one) but after playing a shorter one, the skip loop begin...
By adding the song of the album one by one into iTunes, everything works fine...
I just updated to macOS Catalina (10.15.7) and Music 1.0.6.10 have the same issue.
As a troubleshooting step I would start with booting into Safe Mode to see if the behaviour is replicated there, and also to see if the behaviour continues again afterwards when you've logged back in normally.

Boot into Safe Mode

Follow these steps to boot your Mac into Safe Mode:


Fully shut down your Mac
Restart your Mac
Immediately press the Shift key and keep it down 
Let go of the Shift key when you see the login window (NOTE: If you have FileVault enabled you may need to log in twice).
Take a note of what happens (i.e. can iTunes play and convert full songs or not?)
Now exit Safe Mode by restarting your Mac as normal
Log in normally and test again


Once you've booted into Safe Mode, let me know how you went and we'll go from there.

Test with a new user account

Okay, let's now test to see if this behaviour persists in a newly created user account.


Go to Apple > System Preferences...
Select the Users &amp; Groups preference pane
Click on the plus sign at bottom left (you may need to unlock the padlock first)
Now add the details for the new account and click on the Create User button
Once created, click on Login Options 
Ensure that automatic login is off
Also ensure that the Show fast user switching menu is enabled
Exit preferences


Now log into the newly created account (there should be an option at top right of the menu bar), download an .mp3 file and test iTunes again.

Let me know how you go.