Trouble with reactive.Value containing a mutable object

I've run into some odd behavior and I'm hoping it's user error. I've created a simple app with a reactive.Value() containing a list. Some events trigger reactives that mutate that list (because lists are mutable), and I can see that the list is getting modified, but a UI element that should show the current state of the list isn't being updated. Code below, and working example on shinylive.

from shiny import reactive, render, ui, App


app_ui = ui.page_fluid(
    ui.row(
        ui.column(
            2,
            ui.row(
                ui.input_action_button("add_value", "Add to list"),
            ),
            ui.row(
                ui.input_action_button("remove_value", "Remove from list"),
            ),
        ),
        ui.column(
            10,
            ui.tags.div(id="module_container"),
        ),
    ),
    ui.output_text_verbatim("all_values")
)


def server(input, output, session):
    value_list = reactive.Value([])

    @reactive.Effect
    @reactive.event(input.add_value)
    def _():
        id = "value_" + str(len(value_list.get()))
        ui.insert_ui(
            selector="#module_container", where="afterBegin", ui=ui.input_numeric(id, id, 0)
        )
        value_list.get().append(getattr(input, id))

    @reactive.Effect
    @reactive.event(input.remove_value)
    def _():
        ui.remove_ui(selector=f"#module_container .shiny-input-container:first-child")
        value_list.get().pop()
    
    @output
    @render.text
    def all_values():
        return str(value_list())

app = App(app_ui, server)

all_values() depends on value_list(), and I'm changing the contents of value_list but all_values() isn't updating, even though I can see that the list inside is growing when I click "add to list" because the element label is a function of the length of the list.

Reproduce the supplied app, focusing on reactive.Value([]), the add/remove event handlers, and the all_values() renderer. Trace how the reactive value is read by @render.text and how the in-place list mutations are observed; done when the expected update behavior is established and covered by a regression check.