Looping Apple Account suggestions and "Security Settings Verification" on iMac and how to fix 'Some iCloud Data Isn't Syncing' Issue

Every single time I've turned on or woken my iMac 24-inch, M1, 2021 8GB memory running Sequoia 15.4.1 (and in prior versions) I see a red 2 for Apple Account Suggestions. No matter how many times I enter my user password, these messages switch places; when I click on "Resume Data Sync" & enter my password, that message moves below and the "Security Settings Verification Required" message moves above it. When I then click on "Continue" for "Security Settings Verification Required", I am asked to enter my Mac Password again; when I do that the "Security Settings Verification Required" message moves below the "Some iCloud Data isn't Syncing" message. It's a maddening loop.

***I spent two (2) hours on the phone with an Apple rep in 2023? 2024? who could not fix it.

***I have allowed Web access for iCloud and signed out and then back in to my iCloud account.

***I have four (4) devices (an iPhone 16 Pro v. 18.3.2 now updating to 18.4.1; the iMac 24-inch, M1, 2021 8GB v. 15.4.1 above; an iPad Pro 12.9 v. 18.3.2 right now updating to v. 18.4.1; and an iMac 27" Retina 5k 2020 Sequoia 15.3.2 now updating to 15.4.1); and I think that their settings all match the settings on my phone and each other.

***My internet provider says it's an Apple problem. But maybe I shouldn't have any devices except my phone. Messages is the biggest issue for me.

HELP

[Re-Titled by Moderator]