Hi Arno, a while ago I wrote some notes on using deep-sleep after getting it working with my ESP32-S3 based greenhouse. A series of posts as my knowledge developed.
I use the ESP32-S3 which has dual processors - if the ESP32-C3 doesn’t have the secondary processor you may find it needs more work to get it to wake up.
Re “OTA Mode” … I note you have both a switch and a binary_sensor for this, where I have only the switch.
I suggest you do the maintenance check in the switch … which is automatically executed after wi-fi and API are connected. I found that ESPHome is multi-threaded and so things didn’t always happen in the order I was assuming.
switch:
- platform: homeassistant
name: "OTA Mode"
id: ota_mode
entity_id: input_boolean.shed_ota_mode
# Maintenance check
on_turn_on:
- logger.log: "OTA Mode is ON: Disabling Deep Sleep"
- deep_sleep.prevent: gotosleep
on_turn_off:
- logger.log: "OTA Mode is OFF: Proceeding to sensors"
- deep_sleep.allow: gotosleep
… though one user reported that on_turn_on: didn’t work on their ESP32-C3.
My own greenhouse uses a rain sensor attached to GPIO17 to wake the ESP32 … though it took a lot of fiddling around to get it working correctly 
If I remember correctly it was essential to get all the pin options exactly the same in the deep_sleep and sensor sections.
In case it helps (mainly to show you’re on the right track), this is my code which is working …
sensor:
# rain gauge hardware sends pulses as the bucket tips.
# the pulse_counter component returns the number of pulses in the preceding period (1 minute)
- platform: pulse_counter
name: Rain Gauge
id: rain_gauge
pin:
# Reed switch between GPIO 17 and GND
number: GPIO17
inverted: true
mode: # prevent lots of ON/OFF events
input: true
pullup: true
allow_other_uses: true
# check the rain_gauge every minute while awake
update_interval: 60s
deep_sleep:
id: deep_sleep_1
# wake up if it starts raining while asleep
wakeup_pin:
number: GPIO17 # wake up if a rain gauge pulse is detected
mode:
input: true
pullup: true
inverted: true # the pin is inverted in rain_gauge, so same here
allow_other_uses: true