What al-Arnaut qualified as Sahih
Sho'aib al-Arnaut declared the hadith as Sahih in the isnad, as none would regard any of:
Al-Qa'naby->Malik->ibn Shihab->Salim adn Hamzah sons of -> ibn 'Umar
as untrustworthy narrators. All of them are rather of a high level of trust. However none of them reported the statement of 'umar they rather reported the hadith saying:
"An omen is in a dwelling, a woman or a horse." (Sunan abi Dawod)
Even al-Bukhari and Muslim quoted the
Allah's Messenger (ﷺ) said, "Evil omen is in the women, the house and the horse.'
(Sahih al-Bukhari here via ibn Shihab and here via Malik and Sahih Muslim)
In 'Umdat al-Qary al-'Ayni said that this hadith is matruk from the apparent meaning as else this would mean the prophet() is contradicting himself when declaring omen as shirk. Which means the hadith assuming its authenticity and attribution is correct must not be understood in literal l why rather on the condition of the more correct narration.
Further al-Arnaut explained that this hadith was narrated with the wording:
"If there is evil omen in anything, it is in the house, the woman and the horse."
Which emphasizes a condition and which is regarded more sane (Sahih) as it appears in both Sahih's of al-Bukhari and Muslim (both have been addressed in my reworked answer on the post you are referring to) and many other ahadith imply it too see for example in Sunan abi Dawod and Sunan ibn Majah.
The quote from Musnad al-Farooq
Interestingly ibn Kathir here quoted a narrator chain for a statement of 'Umar that other scholars pretended not too find any. This requires a bit more investigation.
Sho'aib al-Arnaut commented both additions to this hadith from Sunan abi DAwod saying that the narrative of the statement (athar) attributed to imam Malik is Sahih at least the narrators are trustworthy. Please note that he missed to point at the gap between abu Dawod and Malik!
As for the statement (athar) attributed to 'Umar() he said it is quoted in a book of ibn abi ad-Dunya and sahih in Tarikh Baghdad of al-Khateeb al-Baghdadi, however the statement seems to say it is regarded as sahih by al-Khateeb al-Baghdadi (investigation is needed).