Should I use a deeper backbox if the Ethernet cable feels cramped?

Yes, if the installation allows it.

The 21mm and 32mm boxes are the normal surface-box arrangements we use, but there is no prize for squeezing a stiff cable into the shallowest possible space. If the cable or module is being forced into a sharp bend, a deeper compatible backbox gives you more room to dress the cable naturally and usually makes the whole installation less of a wrestling match.