First, I want to thank MacRumors again for bringing light to this issue. Rest-assured, this is indeed an issue and not just a minor annoyance.
My setup: I work from home and do quite a bit of development and testing on my devices (iPhone, iPod touch and a couple of iPads). Mixure of iOS/iPadOS 14 and 15. Some of these devices are also my main devices (e.g. phone) not just used for work.
Home has two Apple TVs. On my devices as well as these Apple TVs, I'm signed in to my iCloud account. I've been the main purchaser of content over the years, so this makes sense (access to such content from my Mac, Apple TVs, etc.).
On iOS/iPadOS 14, Apple had the separate Apple Remote app plus there was a dedicated entry under Settings | Notifications of "Apple TV Keyboard". I had mine turned off. Thus, I never got notifications, but when I needed to (e.g. doing app updates on Apple TV and having to enter my password), it was indeed handy to use my iPhone. But anyone searching say YouTube, never sent a notification to my devices.
Enter iOS/iPadOS 15. As mentioned, that Notifications entry is now gone. Apple also shut off the functionality of Apple Remote since its now part of Control Center. But even when removing Apple Remote from Control Center, notifications will now come to all my devices anytime someone interacts with a text field (or pin-entry field) on Apple TV.
What I find even worse though is even if setting up Apple's new Focus feature, that doesn't help. And these notifications still happen even when my devices are set to Do Not Disturb.
I find it ironic that crucial things such as Amber alerts can be shut off, but these keyboard notifications cannot.
I have since thought of a potential workaround in case Apple refuses to fix this. Basically create another Apple ID (a fake member of the famiy essentially). And as long as that account is part of our Family Sharing, sign in to that account on the Apple TVs. If I try this, I'll report back how that went.