onion puree thickness
For starters, the pasty stuff in your sieve is most likely just fiber from the vegetables. Cabbage and carrots in particular have a lot of fiber and unless you have a really high powered blender, you're not going to break it down enough to pass through a sieve. Most immersion blenders certainly won't be able to do it.

As for the sweetness, usually to bring out the sweetness in vegetables, they are roasted before the liquid is added to make the base of the soup. You could try roasting the carrots and peppers or caramelizing the onions as a prior step.