Constant depth is a different resource question

Every finite circuit has a numerical depth. A constant-depth family claim requires a single depth bound for an unbounded input domain, with a specified gate and ancilla model.

Family 274 is a separate catalogue entry concerning ${\mathrm{QAC}}^0$ parity Scope274. Its claimed obstruction does not by itself obstruct a growing-depth polynomial-size circuit. No reduction from that parity question is established here.

In particular, the $175$-gate finite benchmark is not evidence for constant-depth factoring on arbitrary inputs.