from qgis.PyQt.QtWidgets import QAction, QMenu
from qgis.PyQt.QtCore import QCoreApplication, QEvent

menu_name = "&Repro Menu"

def dump():
    menus = [
        menu for menu in iface.mainWindow().findChildren(QMenu)
        if menu.title() == menu_name
    ]
    print(f"found {len(menus)} menu(s)")
    for index, menu in enumerate(menus, 1):
        print(index, menu, "actions =", [action.text() for action in menu.actions()])

print("before:")
dump()

action = QAction("Temporary Action", iface.mainWindow())
action2 = QAction("Temporary Action2", iface.mainWindow())
iface.addPluginToMenu(menu_name, action)
iface.addPluginToMenu(menu_name, action2)

print("\nafter add:")
dump()

iface.removePluginMenu(menu_name, action)
iface.removePluginMenu(menu_name, action2)
action.deleteLater()
QCoreApplication.sendPostedEvents(None, QEvent.Type.DeferredDelete)
QCoreApplication.processEvents()

print("\nafter remove:")
dump()

before:
found 3 menu(s)
1 <PyQt5.QtWidgets.QMenu object at 0x000002A106B62F00> actions = []
2 <PyQt5.QtWidgets.QMenu object at 0x000002A106B62F90> actions = []
3 <PyQt5.QtWidgets.QMenu object at 0x000002A106B63020> actions = []

after add:
found 4 menu(s)
1 <PyQt5.QtWidgets.QMenu object at 0x000002A106B62D50> actions = []
2 <PyQt5.QtWidgets.QMenu object at 0x000002A106B62DE0> actions = []
3 <PyQt5.QtWidgets.QMenu object at 0x000002A106B62E70> actions = []
4 <PyQt5.QtWidgets.QMenu object at 0x000002A106B639B0> actions = ['Temporary Action', 'Temporary Action2']

after remove:
found 4 menu(s)
1 <PyQt5.QtWidgets.QMenu object at 0x000002A106B62B10> actions = []
2 <PyQt5.QtWidgets.QMenu object at 0x000002A106B62BA0> actions = []
3 <PyQt5.QtWidgets.QMenu object at 0x000002A106B62C30> actions = []
4 <PyQt5.QtWidgets.QMenu object at 0x000002A106B62CC0> actions = []