connection latency from nRF5340 deep sleep to iOS 18

I am trying to keep nRF5340 in sleep state, and wake it up when there's a user input (e.g., button) and send a packet as fast as possible to iOS18. What would be the latency for sending the first packet to iOS, including making a connection to the phone? We assume the device is already paired with the phone.

I asked the question to chatGPT and it says the bottleneck is iOS scanning, which may take a couple seconds, but I'm curious real measurements form experts:

https://chatgpt.com/share/e/68386486-e9ec-8002-af8b-7924ba4d6fe4

Thanks in advance!

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