I need to make this text look like it's somewhat painted on the wall, but the blend if function treats the text in the sun and the text in the shade very differently. How to solve this? I also need to add other things to the wall, and for that the solution of splitting the image up into two does not work.
If layer blending modes aren't doing it for you, or you can't take a new photo, then one possibility is to apply an Exposure Adjustment layer, clip it to the text layer, adjust the exposure to make it darker, then paint in black on the layer mask with a soft edged brush to reveal the area that isn't in the shade.
Let your text layer match well with the sunny part. Insert a Curves adjustment layer which makes the rest of the text darker.
Make a selection with your text before you insert the adjustment layer, it generates the mask automatically, only remove the sunny part.
That was actually already said in the earlier answer. To add some value to this answer I suggest also colorizing the text in the shadow a little blueish because it seems to get most of its light from the blue sky.
Insert a layer filled with a color sampled from the blue sky. Let the layer have blending mode "color burn" and reduced opacity. The layer mask must be the same as in the adjustment layer:
Color burn makes all non-blue relatively darker and everything catches some blue except full 100% white. There's no full white because it's darkened by the adjustment layer.
This can be realistic but I'm afraid somewhere there's someone who expects uniform text visibility. You can work around the light inconsistency problem by making the text self illuminating - a high power modern technology neon sign.