@J0ch3nK
One possibility is that the internal battery in your 1st gen Google Nest Hello Doorbell may have failed. I'm guessing that's what you have, since your post says "Nest app (iOS)". (Yes, it has an internal battery.) The internal battery in each of our 3 Nest Hellos has now failed. The main symptom is that the doorbell goes offline for about a minute whenever the doorbell button is pressed. The purpose of the internal battery is to provide power to the doorbell during the instant when the doorbell button is pressed and power is diverted to ring your indoor doorbell chime.
If you turn off the "Indoor chime" option for your Google Nest Hello Doorbell in the Google Nest app, the doorbell will no longer attempt to ring your indoor doorbell chime and will therefore no longer go offline when the doorbell button is pressed. Since Google Nest will not replace Nest Hellos with failing internal batteries if they are past the 1-year warranty, we have turned off the "Indoor chime" option on all 3 of our Nest Hellos Doorbells and have turned on the "Visitor announcements" option (https://support.google.com/googlenest/answer/7672451) so that we now instead get notifications on our Nest Hubs and Nest Mini whenever any of the doorbell buttons are pressed.
There is a very long locked thread in this forum on this issue, dating back to 2021, with over 1,000 replies:
https://www.googlenestcommunity.com/t5/Cameras-and-Doorbells/Nest-Hello-Doorbell-cuts-out-when-butto...
Some customers have referred to this iFixit post to take their doorbell apart to replace the internal battery after purchasing a replacement battery online. This solution has mixed results, since the doorbell is not really designed to be taken apart.
https://www.ifixit.com/Guide/Nest+Hello+Battery+Replacement/131729
