I just had to look at this youtube video to solve the problem with my bicycle. I just needed to know the right word to search for i.e. “silver shifters” or “down tube shifters“. My levers are not completely made out of steel (“silver”), they rather have a black plastic cover on it so I don’t agree on that term, but I understand down tube shifters. However, “silver shifters” generated way more relevant results for my particular problem. When I realized which word I needed to use to in my research, I had already disconnected the gear wire and adjusted the screws behind the rear derailleur. My initial belief was actually that I just had to tighten the lever (silver shifter) but since I had faced issued with my bicycle over shifting a couple of times lately, I thought that it would be a good opportunity to adjust that as well. I also removed some mud and dust from the frame and raised the saddle a little bit. Those things were actually the best improvements of today’s bicycle maintenance.
The remaining problems that I have is to both adjust the screws back so that the rear derailleur operates in a good manner and make sure that both the gear lever and the wire are tightened. Let’s try to fix it tomorrow. Does anyone know what the correct name is; Silver shifter or Down tube shifter?