Either thing will work tbh.
The crate training theory is based on the principle that a dog won't foul it's bed; so the crate should be set up with the bed filling it completely - either by using a smaller crate or setting up a divider. It isn't perfect, and sometimes they have to wee or poo in the bed because their bladders are so tiny, their muscles are weak, and like children, don't produce the wee reduction hormone at night until they're a bit older.
At 8 weeks I wouldn't entertain a glimmer of hope that she'll be able to go through the night without a loo trip of some sort.
So, to do it theoretically perfectly, you should set an alarm at night to come down for a silent toilet swoop before the dog starts to cry to be let out or just pees regardless. That way, the dog shouldn't learn that loads of noise at night time results in attention from you and means she will never be forced to foul her bed.
That, coupled with trips outside during the day every time she wakes up, after every meal, after every game and pretty much every hour in between should get house training sorted out very fast indeed. In the matter of a week or two.
The other approach is to do what you're doing and in time, she will eventually be able to hold her bladder overnight - probably by the time she's 6 ish months old to be reliable.
The only confusion that your current method will produce is that she's learning that one half of her crate is a toileting area which will take a while to unlearn. She may start using that in the day in preference to going outside and you'll eventually have to teach her not to.
It depends which fits your lifestlye best tbh.
I have done both, depending on the dog. I have also trained with no crate which actually resulted in a cleaner dog faster - but of course that's absolutely dog dependant; our no crate girl absolutely HATED the crate so after just one disaster I folded it away.