I'll try out a few different types of shadows.
Regarding the scaling issue, the "title screen" and the game have different resolutions.
The title screen, actually it was just a image drawn for social media aspects, was drawn on a 210x120 canvas (I guess) and scaled it to a width of 1024 with keeping the aspect ratio. I thought with scaling to this resolution, I won't end up with scaling issues (at least not visible). Now that I took another look, I saw a few issues. So, thank you

The game has a resolution of 288x288, which is exactly 24 (tile size) x 12 (amount of tiles in both ways). When recording, I was cropping the whole game to the relevant things, so the images do not have the same amount of pixels as the game itself. The game window, on the other side, has a resolution of 1024 x 1024.
Currently, I was not thinking about the resolution aspect that much, but I guess, I should change it a bit. Eventually, changing the game resolution (288x288) might be necessary as well, depending on the size of the window. Am I right with the last thought?