There’s a word for this. I knew this was a practice, and it explained a lot about a particular section of the Last Supper, which would have been otherwise inexplicable to me, but I didn’t know there was an actual word. In fact, one of the quotations mentions the Last Supper.
1. The posture of reclining at table, practised by many ancient nations.
1646 SIR T. BROWNE Pseud. Ep. 241 Accubation, or lying downe at meales was a gesture used by very many nations. Ibid. 244 Now there was leaning on Jesus bosome one of his disciples whom Jesus loved; which gesture will not so well agree unto the position of sitting, but is naturall..in the Laws of accubation.
2. Med. Lying in; = ACCOUCHEMENT.