[BUG] callback not triggered when input changes in some configurations

context

dash                 2.18.2
dash-core-components 1.7.1
dash-html-components 2.0.0
dash-renderer        2.0.0
dash-table           5.0.0

Description

The problem I have can be reproduced running the following app:

from time import sleep

import dash
from dash import callback, dcc, html, Output, Input, State

app = dash.Dash(__name__, serve_locally=False)


app.layout = html.Div(
    [
        html.Div("orig",id="display"),
        dcc.Input(id='input', value='Initial Value', type='text'),
        html.Button('Submit', id='submit-btn', n_clicks=0),
        dcc.Store(id="store-1"),
        dcc.Store(id="store-2"),
    ]
)
app.enable_dev_tools(debug=True)
server = app.server

@callback(
    Output("display", "children"),
    Input("store-1", "data"),
    Input("store-2", "data"),
prevent_initial_call=True,
)
def display(store1, store2):
    print(f"display triggered, input ({store1}, {store2})")
    return f"store1: {store1}, store2: {store2}"

@callback(
    Output("store-1", "data"),
    Input("submit-btn", "n_clicks"),
    State("input", "value"),
prevent_initial_call=True,
)
def submit(_, text):
    return text

@callback(
    Output("store-1", "data",allow_duplicate=True),
    Output("store-2", "data"),
    Input("store-1", "data"),
prevent_initial_call=True,
)
def process(text):
    print("process triggered")
    sleep(3)
    print("process ended")
    return (f"processed1-{text}", f"processed2-{text}")

Actual behavior

When I click on the button, I get:
submit callback is triggered -> store-1 modified -> onlyprocess callback is triggered -> eventually process finishes -> store-1 and store-2 modified -> display is triggered

and in the logs I see:

process triggered
process ended
display triggered, input (processed1-Initial Value, processed2-Initial Value)

The first store-1 change should have triggered the display callback directly.

Expected behavior

When I click on the button:
submit callback is triggered -> store-1 modified -> both process and display callback should be triggered at the same time -> eventually process finishes -> store-1 and store-2 modified -> display is triggered

i.e. I should have seen in the logs:

process triggered
display triggered, input (Initial Value, None)
process ended
display triggered, input (processed1-Initial Value, processed2-Initial Value)