Based on everything you have described, this does not appear to be a notification settings issue.
The important detail is that Allow notifications from iPhone enables successfully, but the switch turns itself off after approximately 10 to 15 minutes.
At the same time, the list of supported iPhone apps never appears.
Under normal circumstances, macOS should populate that list shortly after the feature is enabled. If the list never appears and the setting subsequently disables itself, the Mac is usually failing to complete its Continuity registration with the iPhone.
Since you have already confirmed that both devices are signed into the same Apple Account, are connected to the same Wi-Fi network, have Bluetooth enabled, and that Handoff, phone calls, and Messages all work correctly, the usual prerequisites for Continuity appear to be satisfied.
I would first confirm that two-factor authentication is enabled for your Apple Account, as it is required for Continuity features.
Next, disable Handoff on both devices, restart both the iPhone and the Mac, then re-enable Handoff on the iPhone first, followed by the Mac. After waiting a few minutes, enable Allow notifications from iPhone again and see whether the application list appears. Apple provides instructions here:
Hand off tasks between Apple devices - Apple Support
If there is no change, sign out of your Apple Account on the Mac only, restart the Mac, then sign back in.
This forces the Mac to register with Apple's Continuity services again and has resolved similar issues for some users. Apple explains how to sign out here:
If no app is set to open a document on Mac - Apple Support
If the problem persists, start the Mac in Safe Mode and test the setting again.
If the toggle remains enabled in Safe Mode, the issue may be caused by third-party software or a login item. Apple describes how to use Safe Mode here:
Start up your Mac in safe mode - Apple Support
Regarding iPhone Mirroring, that is a separate feature. The absence of the iPhone Mirroring application in the European Union does not prevent iPhone notifications from being forwarded to a Mac. Since your friend receives iPhone notifications without iPhone Mirroring, that is consistent with Apple's implementation.
At this point, because the setting disables itself automatically and the list of supported apps never appears, I would be more inclined to suspect a Continuity registration failure or a software issue in macOS 26.5.2 than an incorrect user setting.
Two questions would help narrow it down further.
Is this a personal Mac, or is it managed by a workplace or educational institution?
This type of setup usually involves a Mobile Digital Management derive like Jamf / Intunes or similar
If you create a new macOS user account and sign into your Apple Account there, does Allow notifications from iPhonestill turn itself off after several minutes?
If the behaviour is identical in a new macOS user account, that would strongly suggest a system-level issue rather than a problem with your current user profile.
Apple also has an overview of the requirements for Continuity features here:
Continuity features and requirements for Apple devices - Apple Support