ah.. i also struggled with that part specifically

달픈 is in adjective form so the standard form should be 달프다, but there’s no such thing in korean. there are two other words 애달프다 (heartrending, the state of pain and regret in heart bc of sth that happened) and 고달프다 (weary, physically and mentally exhausted) which make the adjective form of 애달픈 and 고달픈. so 달픈 alone is kinda ambiguous.

there was this article in namublog which explains the origin of 애달프다, claiming that 애 comes from the chinese character 愛 (love) and 달프다 means sorrow and regret, so 애달프다 means sadness or regret over sth/sb you’ve loved, and it’s usually used when u let go of a loved one or part way (this was the only place i saw 달프다)

there was also this very old ost called 달픈 which contained the lyrics of 달픈마음, and was translated to “aching” and “aching heart” when i looked for it.

i also asked a friend and they said it could be a bland of two words like 달콤한 슬픔 (sweet sadness) or 달콤한 아픔(sweet pain) since koreans often tend to use shorten terms like that (i think that’s what i put in the notes too)

it could be just 애달픈 turning to 달픈 for the sake of poetry and the meter of the lyrics. but considering the previous line which said “as much as i am nervous” or “do you know i am as nervous as i am happy” in previous verses, i thought that was probably the best interpretation due to of the emphasis on both feelings existing at the same time.
so in the end “sweet aching” was what i come up with, and that was why i put **rough trans at the end too. i probably should’ve made a clearer note, but i was literally on autopilot that night, so sorry about that </3