It seems I toke a too short look at al-Bidaya wa an-Nihaya البداية والنهاية as there ibn Kathir has clearly quoted the ahadith from Musnad Ahmad (he quoted two ahadith and a third referring to the second narration) however none of these clearly is explaining the revelation of verse (9:31), but they are describing or telling the story of 'Adi ibn Hatim and how he became a Muslim this excludes a relevance to the linked narration from Jami' at-Tirmidhi. This explains why ibn Kathir didn't quote it in his tafsir and he was not wrong!
Both ahadith are compiled in Musnad Ahamd in the section about the Kufi narrtors (Awwal musnad al-Kufyeen أول مسند الكوفيين) #17796 (here 'Adi was asked to confirm the story of his conversion by a -not named- man) and #18891 (here 'Adi told his story). These ahadith as said have mostly nothing in common with the ahadith related to the revelation of verse (9:31), but you may find them in other sources.
- As for #17796 it is also compiled or partly compiled by al-Hakim in his al-Mustadrak, in al-Mo'ajam al-Kabir of at-Tabarani (twice), a short version is also in sunan ibn Majah, and it also is quoted by ad-Daraqotni in his sunan many times.
while #18891 is compiled or partly compiled in as-Sunan al-Kubra of imam al-Bayhaqi (several narrations), in all three mo'jams of imam at-Tabarni (as-Saghir, al-Awsat and al-Kabir), parts of it especially the statement (or similar statements)
"Protect yourselves from the Fire, even with half a date."
can be found in almost all hadith collections all sunan books (sunan abi Dawod, ibn Majah, an-Nasa'i, ad-Darimi) and tzhe sahihs. Sho'ba (one of the narrators in al-Musnad) showed some uncertainty whether he heard "date" or "part/half a date". Other sources quoting this hadith or parts of it are al-Mosanaf of 'Abdurrazaq, ibn Khozaymah in his sahih al-Bazzar in his Musnad.