So UnsafePackedBinaryWriter relies on a couple of "streaming" data structures, none of which necessarily have a single buffer which contains every sequence of bytes that make up a char stream.
For unescaped sequences that's "fine," you can just serially output data from start to finish and everything will be fine. Two-character escape sequences always start with backslash and aren't too hard to handle either. But unicode escape sequences are between 3 and 6 characters and require substantially more handling to be robust and correct.
I threw together a patch to handle unicode escape sequences but taking a step back this is functionality that, were we really to commit to maintaining, would require a more substantial rewrite of the internals to avoid having to maintain the very fragile "continuation context" necessary to pipeline escaped character state across token boundaries.
Recommendation is for users to use StripStringEscapeCharacters mechanism to strip unicode characters after the data has been linearized.