Thanks @Anabar for sharing this solution. Eight years later, it is still the most comprehensive explanation I found on this matter. Just wanted to append my upgraded version for Python 3.13 and PyQt6; hope it helps.

#!/usr/bin/env python3
# -*- coding: utf-8 -*-

import re
import sys
from PyQt6 import QtWidgets,QtCore,QtGui


class AnimatedLabel(QtWidgets.QLabel):

    def __init__(self,*args,**kwargs):
        super().__init__(*args,**kwargs)

        color1 = QtGui.QColor(255,  0,  0)
        color2 = QtGui.QColor(255,144,  0)
        color3 = QtGui.QColor(255,255,  0)
        color4 = QtGui.QColor(224,192,192)

        color5 = QtGui.QColor(192,224,192)
        color6 = QtGui.QColor(192,192,192)
        color7 = QtGui.QColor(212,208,200)

        self.co_get = 0
        self.co_set = 0
        byar = QtCore.QByteArray()
        byar.append(b"zcolor")

        self.color_anim = QtCore.QPropertyAnimation(self,byar)
        self.color_anim.setStartValue(color4)
        self.color_anim.setKeyValueAt(0.15,color1)
        self.color_anim.setKeyValueAt(0.30,color2)
        self.color_anim.setKeyValueAt(0.50,color3)
        self.color_anim.setKeyValueAt(0.75,color2)
        self.color_anim.setEndValue(color4)
        self.color_anim.setDuration(2000)
        self.color_anim.setLoopCount(1)

        self.color_anim_ok = QtCore.QPropertyAnimation(self,byar)
        self.color_anim_ok.setStartValue(color5)
        self.color_anim_ok.setKeyValueAt(0.50,color6)
        self.color_anim_ok.setEndValue(color7)
        self.color_anim_ok.setDuration(1000)
        self.color_anim_ok.setLoopCount(-1)

        self.custom_anim = QtCore.QPropertyAnimation(self,byar)

    def parseStyleSheet(self):
        ss = self.styleSheet()
        sts = [s.strip() for s in ss.split(";") if len(s.strip())]
        return sts

    def getBackColor(self):
        self.co_get += 1
        return self.palette().color(self.pal_ele)

    def setBackColor(self,color):

        self.co_set += 1

        sss = self.parseStyleSheet()

        bg_new = "background-color: rgba({:d},{:d},{:d},{:d});".\
                format(color.red(),color.green(),color.blue(),color.alpha())

        for k,sty in enumerate(sss):
            if re.search(r"\Abackground-color:",sty):
                sss[k] = bg_new
                break
        else:
            sss.append(bg_new)

        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        # pal = self.palette()
        # pal.setColor(self.pal_ele,color)
        # self.setPalette(pal)
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        self.setStyleSheet("; ".join(sss))


    pal_ele = QtGui.QPalette.ColorRole.Window
    zcolor = QtCore.pyqtProperty(QtGui.QColor,getBackColor,setBackColor)


# this class is only for test
class SomeDia2(QtWidgets.QDialog):

    def __init__(self,*args,**kwargs):
        super().__init__(*args,**kwargs)

        self.co_press = 0

        self.setModal(True)
        self.setWindowTitle("Animation Example")

        self.edit_pad =  QtWidgets.QLineEdit("-1")
        self.edit_rad =  QtWidgets.QLineEdit("-1")
        self._mapHeight = QtWidgets.QLineEdit("0")

        self.layout = QtWidgets.QFormLayout()
        self.lab_pad = QtWidgets.QLabel("Padding (px):")
        self.lab_rad = QtWidgets.QLabel("Radius (px):" )
        self.layout.addRow(self.lab_pad,self.edit_pad)
        self.layout.addRow(self.lab_rad,self.edit_rad)


        self.anila = AnimatedLabel()
        self.anila.setText("Label for animation:")
        self.layout.addRow(self.anila,self._mapHeight)

        self.ok = QtWidgets.QPushButton()
        self.ok.setText("OK -- change animation")
        self.ok.clicked.connect(self._okPress)

        self.layout.addRow(self.ok)
        self.layout.setLabelAlignment(QtCore.Qt.AlignmentFlag.AlignRight)

        self.setLayout(self.layout)
        self.set_initial_data()

    def set_initial_data(self):
        pad_vali = QtGui.QIntValidator(0,20)
        rad_vali = QtGui.QIntValidator(0,10)

        self.edit_pad.setValidator(pad_vali)
        self.edit_rad.setValidator(rad_vali)

        pad,rad = 4,4
        self.edit_pad.setText(str(pad))
        self.edit_rad.setText(str(rad))

        self.set_ss(pad,rad)

        # slots
        self.edit_pad.textChanged.connect(self.change_padrad)
        self.edit_rad.textChanged.connect(self.change_padrad)

    def set_ss(self,pad,rad):
        self.anila.setStyleSheet("padding: 0 {:d}px; border-radius: {:d}px;".\
                format(pad,rad))
        for lab in [self.lab_rad,self.lab_pad]:
            lab.setStyleSheet("padding: 0 {:d}px;".format(pad))

    def change_padrad(self):
        try:
            pad = int(self.edit_pad.text())
            rad = int(self.edit_rad.text())
            self.set_ss(pad,rad)
        except Exception as ex:
            print(type(ex).__name__)

    def _okPress(self,flag):
        self.co_press += 1
        typ = self.co_press % 3
        if 0 == typ:
            print("Animation NO")
            self.anila.color_anim.stop()
            self.anila.color_anim_ok.stop()
        elif 1 == typ:
            print("Animation type 1")
            self.anila.color_anim_ok.stop()
            self.anila.color_anim.start()
        elif 2 == typ:
            print("Animation type 2")
            self.anila.color_anim.stop()
            self.anila.color_anim_ok.start()


if __name__ == "__main__":

    application = QtWidgets.QApplication(sys.argv)
    dialog = SomeDia2()
    dialog.show()
    result = application.exec()