When I added this mod, I can see that that paintings are trying to be transparent, but it isn't fully working. and I see a picture of the wooden painting background, and whatever block is behind. and whenever I move my view, the fuzziness also moves.

I'm using paintings++ To add the custom paintings.

You need to replace the back texture with a fully transparent texture
The only thing this mod does is allow for textures to be transparent on paintings (and other entities).

You need to manually create a fully transparent texture and put it at /assets/minecraft/textures/painting/back.png in your resource pack.