ob-python: Fix async evaluation

* lisp/ob-python.el (org-babel-python-async-evaluate-session): Bind
`python-shell-buffer-name' inside the temp buffer.
* testing/lisp/test-ob-python.el (test-ob-python/async-local-python-shell):
Add test.

lisp/ob-python.el

@@ -400,7 +400,6 @@ by `org-babel-comint-async-filter'."
    session (current-buffer)
    "ob_comint_async_python_\\(.+\\)_\\(.+\\)"
    'org-babel-chomp 'org-babel-python-async-value-callback)
-  (let ((python-shell-buffer-name (org-babel-python-without-earmuffs session)))
   (pcase result-type
     (`output
      (let ((uuid (org-id-uuid)))
@@ -410,7 +409,9 @@ by `org-babel-comint-async-filter'."
          (insert body)
          (insert "\n")
          (insert (format org-babel-python-async-indicator "end" uuid))
-           (python-shell-send-buffer))
+         (let ((python-shell-buffer-name
+                (org-babel-python-without-earmuffs session)))
+           (python-shell-send-buffer)))
        uuid))
     (`value
      (let ((tmp-results-file (org-babel-temp-file "python-"))
@@ -420,8 +421,10 @@ by `org-babel-comint-async-filter'."
          (insert (org-babel-python-format-session-value tmp-src-file tmp-results-file result-params))
          (insert "\n")
          (insert (format org-babel-python-async-indicator "file" tmp-results-file))
-           (python-shell-send-buffer))
-         tmp-results-file)))))
+         (let ((python-shell-buffer-name
+                (org-babel-python-without-earmuffs session)))
+           (python-shell-send-buffer)))
+       tmp-results-file))))
 
 (provide 'ob-python)
 

testing/lisp/test-ob-python.el

@@ -296,6 +296,20 @@ print(list(range(3)))
                      (string= (concat src-block result)
                               (buffer-string)))))))
 
+(ert-deftest test-ob-python/async-local-python-shell ()
+  ;; Disable the test on older Emacs as built-in python.el sometimes
+  ;; fail to initialize session.
+  (skip-unless (version<= "28" emacs-version))
+  (when-let ((buf (get-buffer "*Python*")))
+    (let (kill-buffer-query-functions)
+      (kill-buffer buf)))
+  (org-test-with-temp-text-in-file
+      "# -*- python-shell-buffer-name: \"Python 3\" -*-
+<point>#+begin_src python :session \"*Python 3*\" :async yes
+1
+#+end_src"
+    (should (org-babel-execute-src-block))))
+
 (provide 'test-ob-python)
 
 ;;; test-ob-python.el ends here