What is the ruling on electronic games that contain cards with images of animate beings and immodestly dressed female characters, as well as fictional characters with polytheistic storylines such as sun worship, magic, and attributing divine powers to them, keeping in mind the possibility of muting the in-game music?

What you mentioned by saying: "cards collected by the player the more he plays, to form a set of cards with which he competes with others" – if the intention is to gamble on them, then it is not free from the suspicion of gambling. As for drawings of imaginary animate beings or others, they do not necessitate the prohibition of playing games. If images of women arouse desires, then it is impermissible to play the game; if they do not, then it is not forbidden. As long as doctrinal prohibitions are not present in the game itself, it does not appear that playing it is forbidden merely because there are stories that use the game's characters in a forbidden manner. And as long as the player mutes the music while playing, the game is not forbidden from this aspect.