After looking at some other forums, I found a suggestion to turn off Find My Mac. I did that, and the update worked.

Same here. Mac Mini 2023 M2 Pro, 16 Gb Memory. My response was different. The first time I tried, the download failed and I got this error: Then I restarted and the mack came up like I had just completed an update - Extensions needed permissions, etc. But it still said I had the Beta 4 update to run. so I tried it again. Ir failed on download and I got this same error. I restarted again but machine restarted normally, no request to grant permissions. I tried the update aginind and got the siame error. Maybe there is a problem with Beta 4 with some configurations and Apple is restricting install like with the IOS 18 and the M4 iPad Pro 13" b