Lyn Kidson has added to the considerable amount of secondary literature on 1 Timothy 3:16:
Lyn Kidson, “Naming 1 Timothy 3:16b: A ‘Hymn’ by Another Name?” New Testament Studies 69.1 (2023): 46–56. https://doi.org/10.1017/S002868852200025X
Abstract: Most scholars assume that 1 Timothy 3.16b is a hymn, or a fragment of a hymn, belonging to another context. However, Furley (1995) points out that even the ancients had difficulty categorising their poetic materials. 1 Timothy 3.16b has no metre and neither praises God nor asks him for benefits, which are the usual indicators of a hymn. This article argues that 1 Timothy 3.16b was written by the writer for insertion into the letter, and it was intended to be used in his congregation as a bulwark (1 Tim 3.15) against his opponents. 1 Timothy 3.16b more closely resembles an epigram, normally written to accompany an epiphany of a god.
For earlier literature on 1 Timothy 3:16, see this earlier post.