Does transconductance (Gm) have 3dB bandwidth
Yes, the gm term may also have a frequency dependence which causes it to reduce (or increase in some cases) with increasing frequency. Therefore, the overall gain reduces because of both terms -- ZOUT, and gm.

Generally in individual transistors, the fundamental gm of the transistor element itself have a very high frequency response, but the parasitics around it (including base resistance, gate-drain capacitance) act to reduce the gm observed at the external terminals.