Well, I finally managed to open that damn cover and check the condition of the belt tensioner on my Civic. It turns out it wasn’t loose, but broken. The spring that tensions the pulley snapped. Luckily, the pieces stayed inside the tensioner.
For your information, the cover gives access to the belt tensioner, and with a small mirror or camera, you can see its condition and the belt’s, and adjust it if necessary, but you can’t take it out because the space is too small, so I’ve had to disassemble everything as if I were changing the belt 
Due to my precarious financial situation, I only have enough to buy the new tensioner (€139), and I’m going to keep the same belt, as it still has some service life left and is intact. Also, since I had to remove the VTEC actuator on the side, I checked and the small filter it has is completely clean, with no rubber shavings or anything like that, so…
I’m more and more glad I chose a Honda. With a breakdown of this magnitude, another car wouldn’t even make it 10km.
