This code

var thumbIcon by remember {
   mutableStateOf(if (offer.likedByUser) R.drawable.ic_thumb_up_selected else R.drawable.ic_thumb_up)
}

runs only once, and sets the value to either thumbs_up_selected or thumbs_up. You are not changing the mutableStateOf in your onClick handler, so nothing happens.

You need to change it like this

var thumbIconLiked by remember {
   mutableStateOf(offer.likedByUser)
}

IconButton(
    onClick = {
        thumbIconLiked = !thumbIconLiked
    } 
) {
    Image(
        painter = painterResource(
            id = if (thumbIconLIked) { 
                R.drawable.ic_thumb_up_selected 
            } else { 
                R.drawable.ic_thumb_up 
            }
        )
    )
}