Yes, you can definitely use the APA102 RGB LED on the TinyPICO in ESPHome.
Th code you need to set it up is:
power_supply:
id: rgb_led_power
pin:
number: GPIO13
inverted: true
light:
- platform: fastled_spi
id: rgb_led
chipset: APA102
data_pin: GPIO2
clock_pin: GPIO12
num_leds: 1
rgb_order: BGR
name: "RGB LED"
restore_mode: RESTORE_DEFAULT_OFF
power_supply: rgb_led_power
Which will give you the following results:
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Images & settings provided by Jonny Bergahl