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On Android, especially with Chrome, battery optimization or background restrictions can sometimes prevent things like auto-playing the next track when the screen is off.
You could try the following to see if it helps:
Disable battery optimization for Chrome (Settings > Apps > Chrome > Battery > set to “Unrestricted”)
Make sure background activity is allowed for Chrome
Try a different browser (like Samsung Internet) to see if the behaviour changes
If it continues, it would be due to how the device is handling background playback rather than an issue with the music feature itself.