I understand the general concepts behind CAPsMAN managed CAPs, but what happens to the ethernet interfaces on a device like a hAP Lite? Are those interfaces accessible or managed via CAPsMAN? Is it possible to use CAPsMAN and still configure those ports for use as a local switch?

Any docs that describe this further in detail would be much appreciated. I reviewed https://wiki.mikrotik.com/wiki/Manual:CAPsMAN but didn't find any clear statements on how the non-wireless interfaces behave when configured in this way.

By default (when resetting a device and setting it into CAPS mode) all interfaces are added on the bridge.
Therefor the interfaces are actually in a switch.

CAPsMAN only manages the wireless interfaces.

Hmm, so in order to do a stack of VLANs being broken out on the individual ports and then also managing sets of distinct wifi networks on the device I'd need some more advanced automation than CAPsMAN. My end goal is to find a way to have a series of networks programmatically appear and disappear on specific ports in synchronization with wireless network changes. I know I can do this with terraform managing multiple distinct devices but had hoped it might be possible to do with some more built-in automation layers to manage the multiple devices.

High level: should still be possible.

Low level: a lot more info needed on what you are trying to achieve.
You can completely configure that hAP Lite for VLAN and have the wireless interfaces being managed by capsman and datapath settings.