So, the problem was that after using the "Line in" jack for couple of weeks, the left channel was silent when I switched back to Bluetooth. Both channels did perform normally when plugging the "Line in" jack.
Here's what I did just 5 minutes before writing this message:
1) Grabbed and removed the cushion from the left headphone
2) Ignored the screws which stared at me
3) Tried rotating the left headphone off (like in the image user "arsdezi" posted) but %#*@, it's too tight
4) Ignored the screws again; they're not the ones holding the headphone part
5) Put on my winter gloves and try rotating the left headphone off with even more force: success
6) The "Line in" jack has four contacts; with the tip of a screwdriver, I pressed down the contact that was in the "deepest" end of the jack while the headphones were ON and switched to Bluetooth, to test if the sound finally comes out of the left channel: yes, it did
7) Pressed the contact down with force, while soldering some tin on it to hold it down
8) Assembled everything in place
I've had this problem for a while now and even though I've already stumbled upon this message thread months ago, I had some problems with understanding the repair guides here. Not sure if the problem is that they're written in poor English, or if I just can't read English well enough. Probably both, and more the latter.
For months I thought I had to order a new jack connector, pry open the whole %#*@ thing and hope I could assemble it so that it still would even vaguely resemble the headphones I once had. But the repair wasn't hard at all. Didn't even have to order anything.
EDIT: Also realized, that d - amn is a censored word here, even though the word or it's meaning is not vulgar in nature. #justSJWthings ? :D