It isn’t normal.
The only way a child learns what not to do is negative consequences. The brain literally learns that X behaviour = reward and Y behaviour = causes me to be sad therefore I will do more X and less Y. (This is why computer games are so addictive: they train the brain to seek a fun result.)
If you have zero negative consequences for her bad behaviour then yes, you are doing a bad job of parenting, as a huge part of parenting is training your child to behave in a socially acceptable way. Painting and cuddles is the easy bit, but the less fun parts of parenting are very important too.
If you do have negative consequences for her behaviour, and she is unable to learn from that, ie has no self control, then she might have ADHD. But as you seem unable to say what the negative consequences are, I suspect that is your problem right there.
You don’t have to shout (I don’t), you don’t have to do time outs (I didn’t) you can still cosleep and play and cuddle lots, but you MUSt give negative consequences that upset the child because that is how they learn bad behaviour = makes me sad therefore I won’t do it.
Also, be careful not to give more attention to the child when she is naughty, for example some children actually like being told off as they enjoy the fuss. Find what works for you. I’ve mostly relied on removing fun things. Eg when she was three, my child got cross about a toy and unprovoked hit snother child in the face. I instantly picked her up, said hitting is wrong and you may not hit unless you are attacked and therefore because you hit, no sugar for you for a month. Everybody else can have sweets and cake every day, but not you, because you chose to hit and that is a bad choice. She cried a lot. Fine with me, that means she is learning. That was 5 years ago and she had never hit anyone ever again. She has done other less naughty things and usually that = screentime ban or loss of a fun day out. She does not repeat bad behaviour and she does not mess with me because she knows I will always follow through.
People envy me because my child is so ‘good as gold’ but it was hard work!