According to https://companion.home-assistant.io/docs/wear-os/ -> Complications:
The complications are updated automatically whenever the screen is turned on and roughly every 15 minutes. You can force a complication to update by tapping it on the watchface.
However, this does not work in combination of AOD + TTW. When moving your wrist the display goes on but the complications won't update. With AOD off and TTW on it is working. If AOD and TTW on and you tap the display to wake it, it is also updating as expected.
Wearable: Google Pixel Watch (WearOS 3.5 / June '23 Update)
According to https://companion.home-assistant.io/docs/wear-os/ -> Complications:
The complications are updated automatically whenever the screen is turned on and roughly every 15 minutes. You can force a complication to update by tapping it on the watchface.
However, this does not work in combination of AOD + TTW. When moving your wrist the display goes on but the complications won't update. With AOD off and TTW on it is working. If AOD and TTW on and you tap the display to wake it, it is also updating as expected.
Wearable: Google Pixel Watch (WearOS 3.5 / June '23 Update)