gh-140569: recommend the new REPL in the asyncio REPL docs (#140570)

Co-authored-by: Hugo van Kemenade <1324225+hugovk@users.noreply.github.com>

Doc/library/asyncio.rst

@@ -79,6 +79,10 @@ You can experiment with an ``asyncio`` concurrent context in the :term:`REPL`:
    >>> await asyncio.sleep(10, result='hello')
    'hello'
 
+This REPL provides limited compatibility with :envvar:`PYTHON_BASIC_REPL`.
+It is recommended that the default REPL is used
+for full functionality and the latest features.
+
 .. audit-event:: cpython.run_stdin "" ""
 
 .. versionchanged:: 3.12.5 (also 3.11.10, 3.10.15, 3.9.20, and 3.8.20)