req(False, cancel_output="progress") sends an unexpected recalculated message immediately after progress

[cpsievert]

Here's a fairly minimal example with extended_task, which uses (req(False, cancel_output="progress") under-the-hood).

import asyncio

from shiny import reactive
from shiny.express import app_opts, render

app_opts(debug=True)

@reactive.extended_task
async def slow_compute(a: int, b: int) -> int:
    await asyncio.sleep(3)
    return a + b


@reactive.effect
def handle_click():
    slow_compute(1, 2)


@render.text
def show_result():
    return str(slow_compute.result())

RECV: {"method":"init","data":{".clientdata_output_show_result_hidden":false,".clientdata_pixelratio":2.4,".clientdata_url_protocol":"http:",".clientdata_url_hostname":"localhost",".clientdata_url_port":"51621",".clientdata_url_pathname":"/",".clientdata_url_search":"?vscodeBrowserReqId=1715015365464",".clientdata_url_hash_initial":"",".clientdata_url_hash":"",".clientdata_singletons":""}}
SEND: {"busy": "busy"}
SEND: {"busy": "busy"}
SEND: {"busy": "idle"}
SEND: {"recalculating": {"name": "show_result", "status": "recalculating"}}
SEND: {"progress": {"type": "binding", "message": {"id": "show_result", "persistent": true}}}
SEND: {"recalculating": {"name": "show_result", "status": "recalculated"}}  <--- WRONG!
SEND: {"busy": "idle"}
SEND: {"values": {}, "inputMessages": [], "errors": {}}
SEND: {"progress": {"type": "binding", "message": {"id": "show_result"}}}
SEND: {"busy": "busy"}
SEND: {"recalculating": {"name": "show_result", "status": "recalculating"}}
SEND: {"recalculating": {"name": "show_result", "status": "recalculated"}}
SEND: {"busy": "idle"}
SEND: {"values": {"show_result": "3"}, "inputMessages": [], "errors": {}}

Note that this violates the output progress state machine that we added to shiny.js in rstudio/shiny#4039, which is why the playwright tests are now failing in #1353.