맞아요? Am I correct?

오늘은 <font style="background-color: yellow;">늦게까지 잠을 잤는데도</font> 정말 피곤해요.

 

맞아요? Am I correct?

오늘은 잠 잤어요 하지만 정말 피곤해요.

Hello,

오늘은 잠 잤어요

Today I slept

As you can see here, it doesn't sound natural when you say 'I slept today'  Maybe 'I took a nap today' might be more natural?

That being the case, you may want to use the word '낮잠' meaning 'nap' (literally it means 'Day Sleeping')

So, how about this?

오늘 낮잠잤는데도 정말 피곤해요

잤는데도  = 잤어요.  그런데도 (slept, but still)

Hope this helps!