Output DOCTYPE when calling `WP_HTML_Processor::serialize` on a full document that includes a DOCTYPE.
The DOCTYPE should be included in the serialized/normalized HTML output as it has an impact in how the document is handled, in particular whether the document should be handled in quirks or no-quirks mode.
This only affects the serialization of full parsers at this time because DOCTYPE tokens are currently ignored in all possible fragments. The omission of the DOCTYPE is subtle but can change the serialized document's quirks/no-quirks mode.
Props jonsurrell.
Fixes#62396.
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