I say: In some routes of this hadith in al-Musnad, he is mentioned by this kunya, which indicates that he is indeed Ziyād al-Ḥārithī. Thus, the chain of transmission is authentic. And Allah knows best. The hadith will also come by another route from Abū Hurayrah (1012).
It also has a corroborating report from the hadith of Junādah ibn Abī Umayyah, who said:
“I entered upon the Messenger of Allah, peace and blessings be upon him, on a Friday with a group from al-Azd. The Messenger of Allah, peace and blessings be upon him, invited us to some food before him, but we said, ‘We are fasting.’ He asked, ‘Did you fast yesterday?’ We said, ‘No.’ He asked, ‘Will you fast tomorrow?’ We said, ‘No.’ He said, ‘Then break your fast.’ Then he said, ‘Do not fast Friday by itself.’”
Al-Ḥākim recorded it (3/608) and said, “Authentic according to Muslim’s criteria.” Al-Dhahabī concurred with him.
I say: Its chain includes Ibn Isḥāq, whom Muslim only narrated alongside another narrator. Moreover, he practised tadlīs and related it with ambiguous “from” wording.
982 — “A man’s expenditure on his family, if he seeks reward thereby, is charity.”
Al-Bukhārī (5/17), al-Tirmidhī (1/356)—who said, “Good and authentic”—and Aḥmad (5/273) recorded it from Abū Masʿūd al-Badrī, attributed to the Prophet. The phrase “if he seeks reward thereby” is not found in the first two sources, but it is an authentic and established addition in the two Ṣaḥīḥs and elsewhere.