NB, colourmanagement D Fosse Thank you guys very much for spending time trying to help! I know, for some people it might be easy to understand, apparently I am not one of them. I went through a couple of articles on the internet, and one of the major points there was that color management is basically something you would need for printing your images with accurate colors (the ones you see in the Photoshop). In those articles, they refer to printers as "other devises". My "other devises" are my laptop and my phone. I tried different settings in "Color settings" section, even managed to see colors I wanted for my image in photoshop's preview while saving, using "save for web" option. Still, the image looks different when saved. I also tried the workflow you advised NB, colourmanagement, but unfortunately, it didn't help. I've made some screenshots of my workflow, maybe you could take a look at them and tell me what I do wrong? The screenshot with my settings also attached. Look forward to your reply.
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