I haven't been sleeping vs I haven't slept
Solution 1:
I've been awake for 3 days. I want to paraphrase
Answer
I haven't slept for 3 days.
Reason
A. I haven't been sleeping for 3 days.
My immediate reaction to this as a native speaker is that the person has had difficulty sleeping--over the past three days. They have slept, but only fitfully.
When someone mentions in conversation that they haven't been sleeping, it often means they have been worrying about something and the worry has been keeping them awake.
Real-life examples
I haven't been sleeping lately i have only been sleeping for 3-4 hours a night.. usually i get like 6 hours. This has been going on all this week so far.
I haven't been sleeping the past few days... I just sleep like 5 hours at most and it takes me like 2 hours to fall alseep.
B. I haven't slept for 3 days.
This just means that you have not slept at all.
Solution 2:
Jon hasn't been watching Games of Thrones this season
This means Jon has missed a number of episodes; however, season 8 is still in progress, so Jon could binge-watch and catch up on all the episodes he missed
I haven't been watching TV for three days
This construction is acceptable, it suggests a temporary situation that could change in the future. It generally infers that the speaker did not watch TV for three days or that they watched very little.
I haven't watched TV for three years.
The speaker stopped watching TV three years ago. This non-activity seems deliberate and will probably continue to the future.
Jon hasn't been sleeping well for three nights
In this situation, Jon has been sleeping badly, he probably managed a few hours of sleep but he didn't awake refreshed and rested as he should have.
From The Royal College of Psychiatrists
“There is evidence that cognitive behavioural therapy can be helpful if you haven't been sleeping well for some time”.
Whereas…
I haven't slept for three nights (in a row)
It is possible that the insonnia continues for a fourth night (in which case consult a doctor!) In this case, the inability to sleep is connected to the present (Today I feel like crap. Don't ask me to do anything.)
If we use the simple past tense…
I didn't sleep for three days or nights
Without more context, we might think the speaker is referring to a specific period in their life. The sleepless nights occurred in the past but since then they have had no further episodes of multiple nights of insomnia.