Can't filter DropDown by option value

When I try to filter a DropDown by the value key in the options dict it doesn’t display any matching labels in the DropDown. How ever if I include the value in the option label it will show up. For example I type in 2 into the search box Montreal won’t show up but if I change the label to “Montreal 2” it will. Is there a way to filter the DropDown options by its value without including the value in the label?

Search without the value in the label:

Search with the value in the label:

I’m using dash: 2.0.0, dcc: 2.0.0, html: 2.0.0, dash_table: 5.0.0, plotly: 5.3.1, python: 3.8.3 and Windows.

import dash
from dash.exceptions import PreventUpdate
from dash import html
from dash import dcc
from dash.dependencies import Input, Output

options = [
    {"label": "New York City", "value":1},
    {"label": "Montreal", "value": 2},
    {"label": "San Francisco", "value": 3},

app = dash.Dash(__name__)
app.layout = html.Div([
        "Single dynamic Dropdown",

    Output("my-dynamic-dropdown", "options"),
    Input("my-dynamic-dropdown", "search_value")
def update_options(search_value):
    if not search_value:
        raise PreventUpdate

    return [o for o in options if search_value in str(o["value"])]

if __name__ == "__main__":