I am new to the Arduino maker world.
Having an exposed PCB seems like it asking for trouble
That is a good assumption.
I also do not understand how / what I need to do so that board’s many sensors continue to work. Many of them seem like they need to be exposed to the environment outside of the enclosure
The Arduino board has not been designed to cover special use cases like yours. Its a development board. Companies like Garmin spend a lot of time and resources to create designs where the PCB is sealed inside the watch case and the sensors have exposure to the environment.
For environmental sensors that are not connected to humans its a bit simpler because the conditions are more predictable. The average living room does not go swimming unless you have flooding. The PCB is usually just covered with some coating and the battery compartment has some simple seal.
You can use separate sensors from the PCB and connect them trough wires. Then you need a small compartment inside your case where the sensor is exposed to the environment.