The Messenger of Allah ﷺ said, "Your permission to enter upon me is that you may lift the curtain and listen to my private conversation until I forbid you."Sawadi means his private speech. He granted him permission to hear his private speech.
حدثنا وكيع حدثنا سفيان عن الحسن بن عبيد الله عن إبراهيم بن سويد
قال رسول الله ﷺ إذنك علي أن ترفع الحجاب وأن تستمع سوادي حتى أنهاك سوادي سري قال أذن له أن يسمع سره
Its isnad is sahih. Ibrahim bin Suwayd Nakhai is trustworthy, Nasai deemed him trustworthy, and Ibn Main said, "He is well known." Bukhari gave his biography in Al-Kabir 1/1/290-291. The hadith was narrated by Muslim 2:176. Bukhari also narrated it in Al-Kabir in the biography of Ibrahim bin Suwayd, and Ibn Majah narrated it 1:32.Sawad, with the sin vowelled as "i," means a secret, as Imam Ahmad explained here. See also Nawawi's commentary on Muslim, 14:149-150.