The Prophet ﷺ would not remain seated after his prayer except for the time it took to say, "O Allah, You are Peace, and from You comes peace. Blessed are You, Possessor of Majesty and Honor."
حدثنا يزيد بن هارون قال أخبرنا عاصم الأحول عن أبي الوليد
ما كان النبي ﷺ يجلس بعد صلاته إلا قدر ما يقول اللهم أنت السلام ومنك السلام تباركت يا ذا الجلال والإكرام
Its chain of transmission is sahih. Abu Walid is Abdullah bin Harith Ansari Basri, and he is trustworthy, his hadith being included by the group [of hadith compilers]. The hadith has already been mentioned at 25383.