Code: How can a transfer switch not switch neutrals?
TL;DR: The lack of a switched neutral here has effects on other parts of the system

The presence of a single neutral wire here (which is carrying generator imbalance and providing a 0V point for the wattmeters) means that the generator is relying on the neutral bond in the panel, instead of providing its own. This is important because many portable generators actually come with a neutral bond installed by default (and would need their bond removed to work properly with this transfer switch).  Read on for details.

It means your generator is not a separately derived system

There are two basic configurations for wiring a standby generator.  Either your generator is a separately derived system, which means it provides its own neutral-to-ground bonding point, or it is not a separately derived system, which means it relies on the house it is plugged/wired into to provide the neutral-to-ground bonding point.  This is codified in NEC 702.11, by the way.

Most hardwired generators can be set up either way and left that way without too much difficulty; however, portable generators are pretty much always shipped with their own neutral-to-ground bonding point installed, so they can be safely used as a standalone source of power.  Some generator manufacturers provide instructions for pulling that bond for use  as a standby generator in a non-separately-derived system, but that means that the bond has to be reinstalled if you ever wish to use that generator   for portable power.

But, this fact has ramifications downstream

However, this is not without consequences elsewhere as well.  Many interlocked-breaker feeder-type and all select circuit manual transfer switches, as well as panelboard-type breaker interlock setups, do not provide the extra pole needed to switch the neutral between the two bonding points present in a separately derived standby system, limiting their use to non-separately-derived standby systems.  On the other hand, double throw safety switches can be readily obtained with the extra pole necessary to switch the neutral; there are interlocked-breaker manual transfer switches with a switched neutral as well, such as the Reliance Panel/Link X series and the Eaton CHGEN series.  If you have an automatic transfer switch, note that residential-grade ATSes almost never have a neutral pole of any sort; commercial-grade units are available with a switched neutral pole, but are generally not seen in anything on-topic for this site.

Furthermore, in a non-separately-derived system, all ground and arc fault protection must be downstream of the transfer switch.  This is problematic both at small scales, as some portable generators provide ground-fault protection on both their branch-circuit and their power receptacles and also because it means that ground and arc fault breakers have to be shuffled to a standby subpanel from the panel supplying the utility feeders (or can't be used at all in the case of a select circuit transfer switch), and at large scales, where it interferes with feeder/service equipment ground fault protection on high-current, three-phase, wye-connected feeders and services.

On the flip side, the fact the neutral is broken during the switching process can lead to concerns about voltage spikes with separately derived standby systems; as a result, some switching neutral transfer switches have features to overcome this -- either an overlapped neutral (commonly seen on higher end automatic transfer switches), or a sequentially switched neutral (typically seen on manual transfer switches designed with a dedicated switched neutral pole, such as the Panel/Link X series).