Ensure events are dispatched sequentially

[philippjfr]

Fixes #6603

Supersedes #7115

[codecov]

Codecov Report

Attention: Patch coverage is 10.20408% with 44 lines in your changes missing coverage. Please review.

Project coverage is 72.38%. Comparing base (9404b43) to head (57a0b1b).
Report is 2 commits behind head on main.

Files	Patch %	Lines
panel/io/document.py	10.20%	44 Missing ⚠️

❗ There is a different number of reports uploaded between BASE (9404b43) and HEAD (57a0b1b). Click for more details.

HEAD has 2 uploads less than BASE

Flag	BASE (9404b43)	HEAD (57a0b1b)
	8	6

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #7128      +/-   ##
==========================================
- Coverage   82.25%   72.38%   -9.87%     
==========================================
  Files         327      326       -1     
  Lines       48784    48824      +40     
==========================================
- Hits        40127    35343    -4784     
- Misses       8657    13481    +4824     

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[philippjfr]

Test failures seem unrelated. Will look at making a PR to fix tests next.