macOS Sequoia file compression fails with permissions error for many files

Since the same file compresses successfully when you select a smaller group, I wouldn’t assume that file actually has a permissions problem. Your testing points more toward Finder/Archive Utility failing somewhere in the larger selection.

I’d first make sure Sequoia is fully updated. Apple has made fixes to both Archive Utility and the compression components in later Sequoia updates.

As another test, put those files inside one folder and compress the folder itself instead of selecting thousands of individual files. Finder supports compressing either a folder or multiple selected items.

If compressing the containing folder works, that would help narrow this down to the large multi-file selection rather than the BMP file or its permissions.

Since compressing the folder works, that does make this look more like a Finder issue with a very large multi-file selection than a problem with the files themselves.

If Sequoia is fully up to date and it still happens, I wouldn’t assume a third-party archiver would necessarily have the same problem—it may use a different compression path than Finder.

At that point I’d probably treat another archiver as a workaround rather than keep chasing the permissions message.

I've had various issues creating .zip archives on various platforms so I tend to avoid it for most things these days. And the Finder/macOS can add extra wrinkles. I even limit the number of files I copy at one time because of how flaky the Finder can be.

You may be able to script the process so you don't need any third party software. I'm not sure which Apple method would be the best here since I am not familiar enough with them as I've only dabbled with AppleScript and know even less about any newer options as Automator and Shortcuts, or creating a Quick Action. Some of the newer options may encounter the same problem as they may use the Finder's methods. Even AppleScript could be using the same underlying features for all I know.

With whatever option you end up using, including a third party app, you would want one which logs the failures so you can easily figure out which files still need attention.