Clean up AutoPromptManager vars to be class attributes

[justinchou-google]

b/303489420

[oyj9109]

(No action needed, just leaving a note)
I think ideally, isClosable should be treated as a prompt-level attribute. This change seems fine as we're not going to show multiple prompts within a page.

It might make more sense to rename the attribute to isLocked to indicate the content type of the page. We can think about making this change in the upcoming launch where we support per-prompt dismissibility, to distinguish isClosable attribute at prompt level and isLocked attribute at the page level (which is identical to the class instance).