This is a difficult one, but you really need to eliminate each part of the chain one by one.
If it’s a problem with the file, it will be limited to that file. I think you said it occurs with many files but please confirm.
If it’s a problem with the Pi, you should see the same problem running Raspbian.
If it’s a problem with OSMC, then running Raspbian or LibreELEC may solve it. Then let us know.
If it’s a problem with the TV, then you will be getting two left channels out of the TV speakers (you were asked to check this).
If it’s a problem with the way the TV feeds the headphone output or a mechanical problem with the TV headphone socket, you should get L and R channels through the TV speakers when your speakers are not attached.
This doesn’t normally happen, (although I can reproduce the delay in sound coming back - seems to be new since Leia.) It suggests some poor communication between the Pi and the TV - either the Pi hardware, the cable or the sockets either end.
HTH