I have been trying to install my fully-paid Photoshop Elements 2021 for 2 days. Text help was inable to help and now won't respond. Is there a way to receive a refund from Adobe since this product is now unusable?
That shaking dialogue box is your Mac operating system asking for your local administrator username and password - usually the one you use to log in to your Mac - in order to continue the installation of the software. Nothing to do with Adobe.
I suspect that you are entering your Adobe ID and password which is not what your operating system is asking for, hence the box is shaking.
On a separate note, it's also time to update Big Sur. The current version is 11.6.