This is why I mainly use some other custom <div> with a popover="" attribute. They're easily targeted with a button and no clientside JS required, and can be closed by clicking outside them, which <dialog>s don't have by default. They also still have the same helpful top-layer properties.

Unsure about accessibility on this front, though it can't be worse than my previous attempts with hidden labels/checkboxes/form elements, while being much simpler and less hacky.