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.
iPhone SE (2 gen).
Just get a random message.
iPhone SE 2 gen