Chiming in: 11 year old is the same. I think it's a delay tactic. It usually ends in tears because I just don't have the emotional bandwidth then. Actually rarely now.

Same with almost 13yo DD. During the day I try to ignore the rude comments 90% of the time, but I do call her out when she is really disrespectful. At night I sometimes snuggle and listen to her, but just like you, I am so depleted, I can't do it. I always tell her the night brings all sorts of dark thoughts, let's talk about it tomorrow and it will seem much better. I may start using"worry time" too.

I also find that for my tween, too, bedtime can color her thoughts in a negative way. My own therapist introduced me to the concept of "worry time" where when you have negative thoughts arise when you are trying to get to sleep (or do something else where it's important to calm down), you can tell yourself "save it for worry time." And then have dedicated worry time at a better time of day. Maybe you could even tell your daughter, "tell me the big topics you want to talk about, I'll write them down and then tomorrow we can take a walk and you can really tell me everything on your mind. But for now, it's important that you get some rest." or however you think she'll hear it best

I go through similar issues with a 14 yr old son. Give an inch, they take a mile. I’m exhausted at night too. Tell her you’ll have more clarity in the morning and you want to hear her out and help, but it’s not doable when you’re entirely depleted.

But it’s really important that they feel heard out. My son said I recently upset him when I didn’t listen to him fully. He said I ‘lacked empathy.’