Notifications either do not come at all after updating to iOS15, or they come with a delay of 5 seconds when the application is running in memory. It is the same with other clients after a fresh installation. Other applications (WhatsApp, for example) deliver notifications correctly.
In the latest update of the TG_iOS app (8.1.2), the error is also present, as on my second phone with a clean Telegram. It became uncomfortable to use the messenger for important correspondence.
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Is the badge counter working correctly? Is the delay you described between the badge counter update and the notifications appearing?
So the issue seems to be the missing notification even for received badge counter updates. Right?