Does the game scale with your progress?

I am under the impression that the game gives you harder enemies the more you advance.

At the beginning, I would get mostly red bokoblins, with 1 blue bokoblin per camp, but now, it's mostly blue/black bokoblins, with 1 silver bokoblin per camp. And that is around the 4 main cities, to which you can go at any time of the game, so I guess they should be around the same camp difficulty?

Is it only an impression, or does the game scale up the enemies the farther you progress?

Enemies are not scaled to your game progress. Rather, enemies are scaled to how many enemies you have killed. The more Bokoblins, Moblins, Lynels, etc. that you kill, the more likely you are to encounter blue, black, and silver variants.