Persistent message alert on System Settings icon

Did you try to sign out of your Apple Account in the settings and sign in again after that?

This helped me in the past on my MacBook Pro, running Catalina, but I had to fill in my Apple Account password a couple of times in different dialog boxes.

ahvl wrote:

The Message alert symbol (number 1 in a red circle) on the System Setting icon is still showing after the latest software update on Mac and iPhone despite having performed the download. I can't get rid of it despite looking at all apps and settings. Any clue?

May sound like a silly statement on my part

Downloading an update for either the computer or iPhone is only half of the process in updating

Normally, after a successful download, the computer / Phone will Automatically Shutdown

During the shutdown, it will also normally automatically restart

In doing the Restart that is when the e update actually gets installed

Once that is done, the computer / iPhone may restart numerous times Before it will again automatically boot up with the New Installation

Has this process actual happened ?

My System settings on my MacBook Pro showed a yellow triangle with an exclamation mark in it, and the notification, that I will have to update my Apple Account settings, because some Apple services will be only available after logging in again.

I would suggest to log out of the Apple Account on both devices, restart them and log into the Apple Account again.

Since my MacBook Pro could not be upgraded beyond Catalina, when this happened in the past, I guess that newer Apple Account features on one device require to log out and log in on all connected devices. Especially when you use Passwords or FindMy, which sync information across different firmware versions.

After re-reading you original posting

Can you provide us ( @Ingo271 and self ) a screen shot of this " alert symbol (number 1 in a red circle) "

Be sure Not to include any Personal Information in the image

Use the Image Insertion icon that looks like a TV Screen

Thank you

Perhaps my colleague @Ingo2711 👍 who I believe is more familiar with iOS devices can take a swing that this

I am more macOS and Computer person though do use iOS devices from time to time

It is possible, the macOS System Setting in your image is alerting to a software update that is needed if you are cabling the iPhone to the computer to sync or backup the iPhone to the computer

Have seen this happen and usually occurs when both the iPhone and Computer receive an UpGraded version of macOS / iOS

ahvl wrote:

Yes everything went as per usual with a full restart. The fact that it is on both my Mac and iPhone must mean there is a more general issue...

Respectfully, not necessarily so

To put in context

Currently operate a M4 Desktop, M4 Laptop and M2 Desktop plus an iPhone 15 Pro and not to forget iWatch

Each have been upgraded from previous versions of macOS to current versions of macOS 26.0,26.01, 26.1

The iPhone from iOS iOS 18.6.2, iOS 26, iOS 26.01, iOS 26.1

The iWatch from 11.6.1, 26, 26.02, 26.1

As for a " more general issue . . . "

That would need the Author ( you ) to expand upon that statement, as it is too general a statement

Glad it worked 🙂

Especially multiple, overlapping windows popping up, to put in your Apple Account password, can be a challenge.