My kids are 5 and 9.
They are in bed at about 8:00pm.
By the time they actually fall asleep, eyes closed and passed out... it is about 8:30.
But I get them in bed earlier already... because they like to chat and wind-down first, before they actually actually, fall asleep.
3 year olds, need about 12 hours of sleep. Average. Some need more.
I have found, that whatever the night time routine is... sometimes a child just forces themselves not to fall asleep too soon... because they want to be with you and spend time with you. Even if they are, tired.
YES.... I am sure, your daughter IS exerting enough energy during the day. I assume, she is at Daycare or Preschool? Since you work.
So, with a day like that, at Daycare or Preschool... YES, a child gets a FULL day of being active. They get tired, from their long day too.
As a child gets older, they are more able to force themselves awake... even if they are tired. BUT... some kids (like my son), will actually get more "hyper" the more tired or over-tired they are. Because, they are trying to make themselves, stay up. But they are indeed, tired.
7:40 to 8:00 is only 20 minutes, for pj's/books/singing... and then laying down. MAYBE... start the routine... EARLIER, so that, she gets more time to do those things, without 'rushing' through it.
That is what I would do. Kids, don't like to be 'rushed' through the night routine. They savor being with you and doing those things. So perhaps, start the routine earlier... thus you and she has more time to do it without all the rush. At least for my kids, that is what I need to do.
The less time they have and the more "I" rush them through the night routine... the more, restless they become. And irked.
Also, I would not eat/play/watch cartoons for 1 hour. Do something else that is more active. Even if just in the house. Because, to me, that 1 hour of watching cartoons is maybe, her 'downtime'... then by the time it is bedtime... she is getting her 2nd wind.