Ensure DataModel updates are correctly scheduled

[philippjfr]

DataModel updates were executed even if the Document was locked. Here we correctly schedule these updates.

[codecov]

Codecov Report

Merging #5360 (11aa268) into main (df0b277) will decrease coverage by 0.04%.
Report is 3 commits behind head on main.
The diff coverage is 22.22%.

@@            Coverage Diff             @@
##             main    #5360      +/-   ##
==========================================
- Coverage   72.70%   72.67%   -0.04%     
==========================================
  Files         274      274              
  Lines       39843    39861      +18     
==========================================
+ Hits        28968    28969       +1     
- Misses      10875    10892      +17     

Flag	Coverage Δ
unitexamples-tests	72.67% <22.22%> (-0.04%)	⬇️

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Files Changed	Coverage Δ
panel/io/datamodel.py	47.27% <22.22%> (-3.77%)	⬇️

... and 5 files with indirect coverage changes

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[ahuang11]

I think something might be one off:

async def echo_callback(
    value: Any, user: str, chat_interface: pn.widgets.ChatInterface
):
    await asyncio.sleep(2)

    message_echo = ""
    for character in value:
        message_echo += character
        await asyncio.sleep(0.1)
        yield {
            "avatar": "https://user-images.githubusercontent.com/42288570/246667324-5cf26789-765f-4f76-a8bf-49309d2ae84f.png",
            "user": "OpenAI",
            "value": message_echo,
        }


chat_card = pn.widgets.ChatCard(callback=echo_callback)
chat_interface = pn.widgets.ChatInterface(value=chat_card)
chat_interface.servable()

This video shows me typing 12345 and I expect the response to be 12345 too, but it only goes up to 1234

Screen.Recording.2023-08-01.at.10.43.28.PM.mov

[philippjfr]

I'm not convinced the issue you're reporting is related to this PR. I'll merge for now and then do some more testing.