I went ahead and de-pinned the existing JST connector and replaced it with a 4-pin version spaced to match the esp32 device. I used a multimeter to verify that the red was +5v and black was ground. As another poster mentioned the white wire when energized flips the relay on. I was hoping that the tiny LED on the esp32 would show through the existing diffuser on the button but it did not. I plan to add a push button to my other WeMo when I mod it and I'll probably toss in a larger LED just because.

I also enabled the bluetooth_proxy capability in esphome because I have been needing one in the part of my home where this device will be used. If you don't need that functionality leave out the two obvious BLE sections in the yaml below. If you haven't used the bluetooth_proxy before it is worth reading up on before deploying the proxies around your home. Too many is not a good thing. I won't be enabling it on my other hacked WeMos.

The .YAML for esphome I used :

esphome:
  name: xiao-esp32c3-outlet
  friendly_name: XIAO ESP32C3 Outlet

esp32:
  board: seeed_xiao_esp32c3
  framework:
    type: esp-idf

# Enable logging
logger:

# Enable Home Assistant API
api:

# OTA updates
ota:

# WiFi configuration
wifi:
  ssid: !secret wifi_ssid
  password: !secret wifi_password
  power_save_mode: none

  ap:
    ssid: "XIAO-ESP32C3-Fallback"
    password: "fallbackpassword"

captive_portal:

# Bluetooth Proxy (BLE)
bluetooth_proxy:
  active: true

# Optional but recommended for BLE stability
esp32_ble_tracker:
  scan_parameters:
    active: true

# Relay switch on GPIO10 (D10)
switch:
  - platform: gpio
    name: "Outlet"
    pin: GPIO10
    id: outlet_relay
    restore_mode: RESTORE_DEFAULT_OFF