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I forgot to mention! Host machine is macOS Sequoia 15.0, as is the VM, and Parallels is version 20.0.1 (55659).
I successfully downloaded macOS via the Parallels Control Centre, let it install, logged on as a local user first, then successfully signed into...
.. 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...