Improve validation and permission checks for WP_HTTP_Polling_Sync_Server

[chriszarate]

Harden WP_HTTP_Polling_Sync_Server endpoints to add additional validation and permission checks.

Props @peterwilsoncc for contributions

Trac ticket: https://core.trac.wordpress.org/ticket/64890

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Props czarate.

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[westonruter]

The presence of a validate_callback will prevent the input from being validated against the JSON Schema for the args, unfortunately. This is something which was pointed out to me by @deepaklalwani97 in #10966. See #10966 (comment).

I believe you'll need to explicitly validate against the schema in the validate_callback, as seen in that PR.

[westonruter]

Or maybe this is different since the validate_callback is added at the endpoint level instead of at the arg level? In any case, I wanted to flag it as something to be verified.