def __init__(self):
    super().__init__()
    uic.loadUi('tu_form.ui', self)
    self.btn_a.clicked.connect(self.onClicked)
    self.btn_L.clicked.connect(self.onClicked)
    self.btn_s.clicked.connect(self.onClicked)
    # hacer lo mismo con las demas botones
    [...]
    self.lista = []

def onClicked(self):
    btn = self.sender()
    self.lista.append(btn.text())