serialize
Writes value as application/problem+xml, or returns null if it is not a Problem. That is the interface's way of saying "not mine", which lets ContentNegotiation try the next converter.
As on the JSON side, the contentType this converter was matched under is ignored and the response is labelled application/problem+xml: the media type is the only wire-level marker identifying a problem document. Today the two always coincide, since there is no acceptPlainXml flag. Writing instead of echoing is pinned by a test so that adding one later cannot silently reintroduce the bug the JSON converter shipped with.
The response is always UTF-8, whatever charset was negotiated. An XML document states its own encoding in-band and ProblemXml writes that declaration as a literal encoding="UTF-8", so honouring a negotiated ISO-8859-1 would put latin-1 bytes inside a document claiming to be UTF-8. That is wrong for anything reading the bytes without the HTTP header, which is any parser handed a saved file or a queued message.