Time Machine issue . . .

...adding an additional external drive, and moving some large items to that external drive. Like Music, videos, pictures, but NOT applications.

<< I'm seeing the same problem immediately after updating to Tahoe 26.1 >>

Then your solution should be found above.

if your situation is not identical, please describe how it is different.

I'm seeing the same problem immediately after updating to Tahoe 26.1

That is not likely to be a drive problem.

You generally see that message when you have linked the files on your Mac to your iCloud account, and are storing the Master copy of the file on iCloud. This feature is called "Optimize Storage".

But as you are now seeing, the setup has some unexpected issues. In addition, using Optimize storage is like an addiction, and is VERY hard to stop storing files on iCloud. [in my opinion] far superior long term results are obtained by adding and additional external drive, and moving some large items to that external drive. Like Music, videos, pictures, but NOT applications.

To be able to complete the backup, you Mac must spend enough 'awake but not too busy' time, logged in with the Apple-iD that owns those files, to fetch the Master copies of those files down from iCloud and allow the backup to complete.

This isn’t a bad Time Machine disk, and erasing it won’t fix the root cause.

What’s actually happening is macOS thinks some of your files are iCloud-only placeholders, and Time Machine refuses to back up data it can’t read locally, even though you’re logged in and everything looks unlocked. The “no permission” message usually points to an iCloud ownership or sync-state mismatch, often triggered after an OS update like Tahoe 26.1. The practical fix is to force macOS to make those files truly local again, go to System Settings > Apple ID > iCloud > iCloud Drive, turn off Optimize Mac Storage, then leave the Mac awake, plugged in, and logged into the correct Apple ID until Finder finishes downloading everything.

If certain folders still won’t download, right-click them in Finder and choose Download Now while watching the cloud icon status. Once the files are local, Time Machine will resume normally on that drive.

If the other TM disk works, that’s just timing; one disk hit the unreadable files first. Only consider erasing after you’ve confirmed all iCloud-backed files are fully local and the error still persists, which in cases like this is rare.

I find that interesting. I had alternating hourly backups but since Tahoe only one of the drives is hourly and the other has a rest. If I use the computer the hourly backing up shifts to the other drive. I do not get an error message.

My data is all on the Cloud because I have computers scattered around the house, at work, etc. and it is a convenient way to share my up to date data.

I use both drives to make sure old data is accessible. I know the Time Capsule is soon to be redundant and have been worried that it is ancient.

I was not too concerned about the issue but it is a bit of a worry.

Guy

<< but since Tahoe only one of the drives is hourly >>

Recent versions of macOS keep Time Machine snapshots (compact lists of links to files) on the boot drive, to reduce the amount of disk I/O to the external, that might high slow down your Mac while you are using it.

I think you will find the algorithm is more complex than "one gets a rest".

Time Capsule features deprecated:

The Server protocol that talks to Time Capsule Server is what is being removed. You could extract that Time capsule physical drive and place it in a USB enclosure to keep using it.

If you Erase it in place, Tahoe will NOT re-use it inside the Time Capsule.

any Mac computer running MacOS 10.13 High Sierra or later can be pressed into service as Shared Time Machine Backup destination.

Back up to a shared folder with Time Machine on Mac - Apple Support