`private class` fails to initialize the type's namespace

Prerequisites

Please put an X between the brackets as you perform the following steps:

• Check that your issue is not already filed:
  https://github.com/leanprover/lean4/issues
• Reduce the issue to a minimal, self-contained, reproducible test case.
  Avoid dependencies to Mathlib or Batteries.
• Test your test case against the latest nightly release, for example on
  https://live.lean-lang.org/#project=lean-nightly
  (You can also use the settings there to switch to “Lean nightly”)

Description

After defining a private class or structure either via an explicit private or through the module system, a user cannot open or export from the type's namespace, because it has yet to be initialized.

Context

This issue was discovered during the port of Lake to the module system (#9749).

Steps to Reproduce

prelude
import Init.Notation

private class Foo where
  foo : Nat

/-- error: unknown namespace 'Foo' -/
#guard_msgs in export Foo (foo)

/-- error: unknown namespace 'Foo' -/
#guard_msgs in open Foo (foo)

namespace Foo end Foo

open Foo (foo) -- works
export Foo (foo) -- works

This example occurs with both class and structure and, in a module, without an explicit private.

Expected behavior:

open and export work without needing to first define the namespace.

Actual behavior:

Namespace must first be explicitly defined before open or export work.

Versions

leanprover/lean4:nightly-2025-08-22

and recent master (f12177d01e)

Impact

Add 👍 to issues you consider important. If others are impacted by this issue, please ask them to add 👍 to it.

Start by running the minimal reproduction from the issue against the referenced Lean nightly or current master, focusing on private class/structure declarations followed by open and export. The fix is complete when those commands work without an explicit namespace Foo declaration, including the module-system case, while the existing reproduction remains valid.