dash_duo does not work with All-in-One components

dash                      2.1.0
dash-bootstrap-components 1.0.3
dash-core-components      2.0.0
dash-html-components      2.0.0
dash-table                5.0.0
pytest                    7.0.1

Describe the bug

It seems that dash testing utils don't work property with All-in-One components. For instance, given the following test scenario:

import uuid
from typing import Optional

import dash
from dash import MATCH, Input, Output, callback, html


class SomeButton(html.Button):
    class ids:
        button = lambda aio_id: {"component": "SomeButton", "aio_id": aio_id}

    def __init__(self, aio_id: Optional[str] = None):
        if aio_id is None:
            aio_id = str(uuid.uuid4())

        super().__init__(
            "Loading...",
            id=self.ids.button(aio_id),
            disabled=True,
        )

    @callback(
        Input(ids.button(MATCH), "children"),
        output=dict(
            label=Output(ids.button(MATCH), "children"),
            disabled=Output(ids.button(MATCH), "disabled"),
        ),
    )
    def update_button(_):
        return dict(label="Loaded", disabled=False)


def test_some_button_first_time(dash_duo: dash.testing.composite.DashComposite):
    app = dash.Dash("foo123")
    app.layout = html.Div(SomeButton(), id="wrapper")

    dash_duo.start_server(app)
    dash_duo.wait_for_contains_text("#wrapper", "Loaded")


def test_some_button_second_time(dash_duo: dash.testing.composite.DashComposite):
    app = dash.Dash("bar123")
    app.layout = html.Div(SomeButton(), id="wrapper")

    dash_duo.start_server(app)
    dash_duo.wait_for_contains_text("#wrapper", "Loaded")

The first run test_some_button_first_time is perfectly fine. But test_some_button_second_time results with selenium.common.exceptions.TimeoutException: Message: text -> Loaded not found inside element within 10s error.
I ran it with --pause option and in the DevTools I noticed that for the second test the update callback _dash-update-component is not being triggered (see the attached screenshots).

Moreover, if I run test_some_button_second_time separately or if I comment out the first test everything is fine.
For some reason callbacks are fired only for the first test.

Expected behavior

It seems that dash_duo does not work with @callback for all-in-one components.

Screenshots

Reproduce the issue with the two test functions shown, using dash_duo and SomeButton, and compare the first and second runs in the browser. Trace the dash.testing composite behavior around @callback and the _dash-update-component request. Done means both tests pass together and the second test triggers its update callback without requiring isolation.