Elaborate on callback exception summary

[ahuang11]

Based on feedback from
https://discourse.holoviz.org/t/chatinterface-streaming-error-with-langchain/6589/4
"""
Thank you for your help. Did not know about callback_exception=“verbose”
"""

and
https://www.youtube.com/watch?v=mFmPDyLlj1E:
"""
The simple case works, but when I ask my agents to write code, I get an error in Panel chat. I know the code has run successfully by looking at the terminal. But in the Panel chat it shows a message with Avatar symbol as red X, avatar name 'Exception', and the message content is just the literal string 'name'.
"""

I think users get stuck when errors occur; this PR elaborates on next steps to unblock them.

import panel as pn
pn.extension()

def callback(content, user, instance):
    1 / 0

pn.chat.ChatInterface(callback=callback).servable()

Eventually, I think I want to allow users to add a custom exception handler #6047

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (3448cdd) 84.67% compared to head (7587ac7) 84.64%.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #6046      +/-   ##
==========================================
- Coverage   84.67%   84.64%   -0.04%     
==========================================
  Files         291      291              
  Lines       43816    43816              
==========================================
- Hits        37101    37087      -14     
- Misses       6715     6729      +14     

Flag	Coverage Δ
ui-tests	40.64% <0.00%> (-0.01%)	⬇️
unitexamples-tests	72.83% <100.00%> (-0.03%)	⬇️

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