Short answer: you can't get a real inline dropdown in Designer's Property Editor from pure Python. That specific bit needs a compiled C++ plugin. But there's a Python path that works well in practice — I'll explain both.

What doesn't work (so you can skip the dead-ends I hit):

I tried a QDesignerPropertySheetExtension to swap the property's editor. On PySide6 6.11:

• You can't delegate to Designer's built-in sheet — extensionManager().extension(...) hands it back as a bare QObject and shiboken can't recover the real interface, so the methods just aren't there.
• Replacing the sheet wholesale with a Python-built one segfaults Designer during form load — even when every property returns a plain string. Its core assumes the internal C++ sheet.

Also worth knowing: declaring the property as a Q_ENUM/@QEnum does give you a dropdown, but only for static, compile-time enums baked into the widget. It's no help if your options are computed at runtime (mine come from a project file), which was the whole point.

What actually works — a task-menu extension:

Right-click the widget → your action pops a combo box → you write the choice back through the form cursor. It's undo-aware, dirties the form, and saves to the .ui like any normal edit.

from PySide6.QtDesigner import (QExtensionFactory, QPyDesignerTaskMenuExtension,
                                QDesignerFormWindowInterface)
from PySide6.QtGui import QAction
from PySide6.QtWidgets import QInputDialog

TASKMENU_IID = "org.qt-project.Qt.Designer.TaskMenu"

class ThemeTaskMenu(QPyDesignerTaskMenuExtension):
    def __init__(self, widget, parent=None):
        super().__init__(parent)
        self._widget = widget
        self._action = QAction("Set theme…", self)
        self._action.triggered.connect(self._choose)

    def taskActions(self):
        return [self._action]

    def _choose(self):
        names = ["Light", "Dark", "Solarized"]      # build this list at runtime
        current = self._widget.property("appTheme") or ""
        i = names.index(current) if current in names else 0
        name, ok = QInputDialog.getItem(self._widget.window(),
                                        "Theme", "Theme:", names, i, False)
        if not ok or not name:
            return
        fw = QDesignerFormWindowInterface.findFormWindow(self._widget)
        # cursor path = undoable + saved to the .ui; a raw setProperty won't stick
        (fw.cursor().setWidgetProperty(self._widget, "appTheme", name)
         if fw else self._widget.setProperty("appTheme", name))

class ThemeTaskMenuFactory(QExtensionFactory):
    def createExtension(self, obj, iid, parent):
        if iid != TASKMENU_IID or not isinstance(obj, MyCustomWidget):
            return None
        return ThemeTaskMenu(obj, parent)

Register it in your plugin's initialize(core):

core.extensionManager().registerExtensions(
    ThemeTaskMenuFactory(core.extensionManager()), TASKMENU_IID)

Two things that bit me:

• Apply via fw.cursor().setWidgetProperty(...), not just widget.setProperty(...) — otherwise the change never makes it into the saved .ui.
• Keep the underlying property a plain, validated @Property(str). The menu is only an input aid; the stored value stays portable and works fine on machines without your plugin.
• If you have both PyQt5 and PySide6 installed, launch designer with QT_API=pyside6 or qtpy may pick PyQt5 and your plugin import will fail.

So: static enum → Q_ENUM. Runtime options → task-menu extension. True inline dropdown → C++ only.

I use a slightly fancier version of this (a little dock with a combo per property) in my widgets library if anyone wants a fuller reference:
https://github.com/SpinnCompany/QT-PyQt-PySide-Custom-Widgets

Marking this solved — hope it saves someone the segfault hunt.

I also attempted the example below which didn't work as I expected:

class QCustomCheckBox(QCheckBox):
    @QEnum
    class EasingCurveEnum(Enum):
        Option1 = 0
        Option2 = 1
        Option3 = 2  
        
    def __init__(self, parent=None):
        super().__init__(parent)

        self._easing_curve = EasingCurveEnum.Option1
        # ...

    @Property(EasingCurveEnum, designable=True)
    def animationEasingCurve(self):
        return self._easing_curve
    
    @animationEasingCurve.setter
    def animationEasingCurve(self, curve):
        self._easing_curve = curve

Images showing my custom properties:

Your enum needs to be part of a QObject based class... otherwise moc / QtDesigner won't notice it.
Check the indentation in my linked example. It's part of the QObject class, not a standalone Python enum class.

Edit:
What @JonB wrote above :D

The enumerator must be in a QObject derived class to be registered.

I know no more than that, nor whether this is the right approach. Try moving your class EasingCurveEnum(Enum) inside class QCustomCheckBox(QCheckBox).

@QEnum
class EasingCurveEnum(Enum):
....

I tried it didnt work.

I also tried this, did not work either:

class EasingCurveEnum(Enum):
    Option1 = 0
    Option2 = 1
    Option3 = 2

class QCustomCheckBox(QCheckBox):
    def __init__(self, parent=None):
        super().__init__(parent)
        
         #tried.....
        QEnum(EasingCurveEnum)

        self._easing_curve = EasingCurveEnum.Option1
        # ...

    @Property(EasingCurveEnum, designable=True)
    def animationEasingCurve(self):
        return self._easing_curve
    
    @animationEasingCurve.setter
    def animationEasingCurve(self, curve):
        self._easing_curve = curve

I guess the same way as in C++. You need to register the enum.

When using Python enums, with @QEnum

• https://doc.qt.io/qtforpython-6/PySide6/QtCore/QEnum.html