Log handler system isn't thread safe

[TPGamesNL]

The current system for log handlers is not thread safe, due to its design. Two relatively long-lastig log handlers from seperate threads could cause problems when their timing intersects. Below is an example to demonstrate this issue:

function useLogHandler():
	set {_a} to "cowcowcowcowcowcowcowcowcowcowcowcow"
	set {_l::*} to {_a} parsed as "%entity type%%entity type%%entity type%%entity type%<.+>"

command /async:
	trigger:
		create section stored in {_section}:
			# Code below will be ran async, it lasts a couple seconds on my machine, giving the user time to reload a script
			broadcast "&eStarted using log handlers"
			loop 10 times:
				useLogHandler()
			broadcast "&eDone using log handlers"
		run section {_section} async

Reproduce by executing the command, then reloading a script file.
Examples of errors which may occur: https://pastebin.com/dfPAb3Sd

While it is unlikely for someone to require parsing a string with the word 'cow' 12 times as entity types on a seperate thread, in unlucky occasions, this problem could crash the server / spam the console (I've seen it happen at least once before, possibly also caused #3291).

I'm not sure how the current system could be improved to avoid this issue, since simply making it no longer based on the list's order will, instead of erroring, cause log entries to be logged to the wrong handler.