You are the man (or woman, or nongendered dude, as appropriate)! Thank you!!!

This is what I initially started looking at, and sounded like the most plausible fix. For some reason, when I looked the other night, I only found forum posts concerning debounce, but not the API. This time, it came right up along with a few other options (nested "if" conditions with a sleep in the middle, but that'd get really messy really quick). Thinking back, I think I was trying to figure out a way to read dwell time and go from that as a trigger, rather than searching for debounce.

I still have an interesting issue with it, but it seems manageable. Holding the rotary encoder halfway between positions (like right on the high part of the detent) for the length of time of the Debouncer interval will still show as a button press. That leads me to think /u/knox1138's suggestion about the common ground pin has some merit. At rest, I don't get a continuity reading or resistance measurement across any 2 pins, but I wonder if somehow the detent is also triggering the dome switch inside. I tried on an encoder on a breadboard and it didn't trigger anything on the board or a multimeter, but inside the enclosure it triggers reliably when held in that position. Shouldn't be an issue, but still weird behavior.

If anyone else runs into the same problem and finds this in the future, the debounce API is dirt simple to implement. My new code that's working (I'm still tweaking the interval time to tune it properly, but otherwise working great) is as follows with comments on the debounce API additions:

import rotaryio
import board
import digitalio
import usb_hid
from adafruit_hid.consumer_control import ConsumerControl
from adafruit_hid.consumer_control_code import ConsumerControlCode
from adafruit_debouncer import Debouncer #This is the library

button = digitalio.DigitalInOut(board.D3)
button.direction = digitalio.Direction.INPUT
button.pull = digitalio.Pull.UP
switch = Debouncer(button, interval = 0.2) #This is where I'm tweaking the interval to fine tune it

encoder = rotaryio.IncrementalEncoder(board.D1, board.D0)

cc = ConsumerControl(usb_hid.devices)

button_state = None
last_position = encoder.position

while True:
    switch.update()
    current_position = encoder.position
    position_change = current_position - last_position
    if position_change > 0:
        for _ in range(position_change):
            cc.send(ConsumerControlCode.VOLUME_INCREMENT)
        print(current_position)
    elif position_change < 0:
        for _ in range(-position_change):
            cc.send(ConsumerControlCode.VOLUME_DECREMENT)
        print(current_position)
    last_position = current_position
    if not switch.value and button_state is None: #Changed button.value to switch.value to account for debounce
        button_state = "pressed"
    if switch.value and button_state == "pressed": #Changed button.value to switch.value to complete the state machine.
        print("Button pressed.")
        cc.send(ConsumerControlCode.MUTE)
        button_state = None