[lldb][NFC] Move SBThread::ResumeNewPlan out of the header (#151988)

This *private* method is only defined as a member class of SBThread so
that it may be declared a `friend` of SBError and access a private
constructor of SBError that takes a `Status`, which is an `lldb_private`
object. In other words, the method does not use anything about the class
is belongs to, so it has no business being a member method.

A subsequent patch will need to add a new argument to this class, a
`Process::StopLocker`, which is also another `lldb_private` object. This
is another strong suggestion that this method does not belong on the
header file of a public API, even if at the private visibility level. We
can't forward declare nested types like `Process:StopLocker`, so this
problem is not easily solvable.

This commit moves the method out of the header and into an anon
namespace of the cpp file. It is also made to return a Status instead,
and the private `SBError` constructor is accessed by the SBThread
methods that call it.

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