I'm working on a commercial HVAC system that has a fan coil unit (FCU) fed by hot and cold water from a rooftop boiler/chiller system. There is an old pneumatic room thermostat that opens/closes the pneumatically-actuated valves, which regulate the flow of hot and cold water into the FCU. The thermostat and one of the pneumatic valves have failed and the valve is obsolete, so there's no repair kit available to fix it. I intend to replace the pneumatic valves with electric motorized zone control valves and replace the thermostat with an electronic internet-connected "smart" thermostat.
The old system has a 4" steel junction box that has mounted on it a combination transformer & contactor made by Honeywell. Power comes into this box from the branch circuit and goes through FMC to an Intermatic-type mechanical timer (which also serves as a disconnect). The switched power then returns through the FMC back to the 4" steel box.

The switched power wires are connected to the primary leads of the 24 VAC transformer. The 24V power outputs to screw terminals mounted on the outside face of the transformer, but the output wires re-enter the steel box through a hole in the mounting plate and plug into the coil terminals for the contactor. The contactor then switches the power to the fan motor.

So, already there is high voltage and low voltage mixed inside the 4" steel box, and this appears to be by design by Honeywell. But admittedly, the low-voltage power doesn't go very far and never leaves the enclosure.
For my retrofit, I need 24 VAC to power both the thermostat and the control zone valves; there will be a new separate enclosure containing relays that will take the output signals from the thermostat and use the relays to control the valves. There will also be a relay in this new enclosure that will control the existing contactor, so the new thermostat can also control the fan.
I have 16/4 cable to bring the 24 VAC power from the existing transformer to the new enclosure (2 wires) and to return the switched power from the new fan relay to the existing contactor (2 wires). Can the 16/4 cable enter the 4' steel box and connect to the blue 24 VAC wires from the transformer inside the box, or must I make the connection on the outside of the box using the screw terminals on the face of the transformer? Either way, I have to bring the two switched 24 VAC wires into the box to connect to the contactor coil terminals.
The old system has a 4" steel junction box that has mounted on it a combination transformer & contactor made by Honeywell. Power comes into this box from the branch circuit and goes through FMC to an Intermatic-type mechanical timer (which also serves as a disconnect). The switched power then returns through the FMC back to the 4" steel box.

The switched power wires are connected to the primary leads of the 24 VAC transformer. The 24V power outputs to screw terminals mounted on the outside face of the transformer, but the output wires re-enter the steel box through a hole in the mounting plate and plug into the coil terminals for the contactor. The contactor then switches the power to the fan motor.

So, already there is high voltage and low voltage mixed inside the 4" steel box, and this appears to be by design by Honeywell. But admittedly, the low-voltage power doesn't go very far and never leaves the enclosure.
For my retrofit, I need 24 VAC to power both the thermostat and the control zone valves; there will be a new separate enclosure containing relays that will take the output signals from the thermostat and use the relays to control the valves. There will also be a relay in this new enclosure that will control the existing contactor, so the new thermostat can also control the fan.
I have 16/4 cable to bring the 24 VAC power from the existing transformer to the new enclosure (2 wires) and to return the switched power from the new fan relay to the existing contactor (2 wires). Can the 16/4 cable enter the 4' steel box and connect to the blue 24 VAC wires from the transformer inside the box, or must I make the connection on the outside of the box using the screw terminals on the face of the transformer? Either way, I have to bring the two switched 24 VAC wires into the box to connect to the contactor coil terminals.