Don't track private symbol roots in other files during js declaration emit

[weswigham]

Fixes #55375

The linked issue only repro'd with strict: false and strictNullChecks: true because without those set, we'd reuse input type nodes much more, and not reprint the union type for the field in the Option type. When we traverse that field, we'd see the Test member in another module, and mistakenly try to add it as something to print in the current file. Now, we have guards against actually doing that already, but traversing it at all caused us to reserve the Test name for that symbol in the index file, and thus mangle the original Test name for the other symbol when we reprinted the import in the file later.