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.. apologies, my post is strictly not related to the AppleID login issue, but for me, I wanted to do both things - AppleID Login within the VM +...
There's a path to upgrading the vanilla Parallels macOS image to Sonoma 14 Beta 3 here .....
I tried this first with little success, then worked out my own fix. https://gist.github.com/mag911/1a5583a766467d6023584d738cee0d98 Hope it works...