Hi, I have a guest bathroom with two entrances and two Nuki Ultra locks.
Both locks should always stay in sync: when one lock opens, the other one should open too, and when one lock closes, both locks should close.
This is just a guest bathroom, so there’s no real security risk — unless someone is planning to steal my toothbrush.
ChatGPT suggested solving this via a hub and an API integration, so that any action on one lock automatically triggers the same action on the other lock.
Yes, you can easily achieve this by pairing both locks to a Smart Home hub (e.g. Apple Home Pod via Matter, Raspberry Pi via WIFI/MQTT or Matter/Thread and Home Assistant) and set up an automation there. Nuki itself currently does not provide automations for such a use case.
Ok, but it doesn‘t work with Alexa, correct? So for example I use this:
Home Assistant Green – Hub Casa Smart – Very affordable home assistant hub, perfect for local automations including Nuki integration. 
This allows you to install Home Assistant OS directly, integrate Nuki via API, and create your synchronized door automations. Or Raspberry Pi? What would be your favorite?
Simple automations like “if this than” should work on all platforms.
Home Assistant is very powerful and allows to do more complex automations, but is also more complex to set up and configure.
I would always use something with Matter and Thread support as it prolonges the battery life of the Smart Lock significantly in comparison to a WiFi based setup. Apples HomePod should work well if easy usability is what you want. Home Assistant Green with ZBT-2 is the most flexible option.