Various TG Chat message sorting fixes (#25229)

* Fixes unsorted emotes, announcements, votes, surgery, prayers, ahelp responses

* Apply suggestions from code review

Co-authored-by: Burzah <116982774+Burzah@users.noreply.github.com>

---------

Co-authored-by: Burzah <116982774+Burzah@users.noreply.github.com>

code/modules/admin/misc_admin_procs.dm

@@ -27,7 +27,7 @@ GLOBAL_VAR_INIT(nologevent, 0)
 	for(var/client/C in GLOB.admins)
 		if(R_ADMIN & C.holder.rights)
 			if(important || (C.prefs && !(C.prefs.toggles & PREFTOGGLE_CHAT_NO_TICKETLOGS)))
-				to_chat(C, msg, MESSAGE_TYPE_ADMINPM, confidential = TRUE)
+				to_chat(C, msg, MESSAGE_TYPE_ADMINCHAT, confidential = TRUE)
 			if(important)
 				if(C.prefs?.sound & SOUND_ADMINHELP)
 					SEND_SOUND(C, sound('sound/effects/adminhelp.ogg'))

code/modules/admin/verbs/adminpm.dm

@@ -223,10 +223,10 @@
 		if(X.key != key && X.key != C.key)
 			if(message_type == MESSAGE_TYPE_MENTORPM)
 				if(check_rights(R_ADMIN|R_MOD|R_MENTOR, 0, X.mob))
-					to_chat(X, third_party_message)
+					to_chat(X, third_party_message, MESSAGE_TYPE_ADMINPM)
 			else
 				if(check_rights(R_ADMIN|R_MOD, 0, X.mob))
-					to_chat(X, third_party_message)
+					to_chat(X, third_party_message, MESSAGE_TYPE_ADMINPM)
 
 	//Check if the mob being PM'd has any open tickets.
 	var/list/tickets = tickets_system.checkForTicket(C, ticket_id)

code/modules/admin/verbs/pray.dm

@@ -34,7 +34,7 @@
 
 	for(var/client/X in GLOB.admins)
 		if(check_rights(R_EVENT,0,X.mob))
-			to_chat(X, msg)
+			to_chat(X, msg, MESSAGE_TYPE_ADMINPM)
 			if(X.prefs.sound & SOUND_PRAYERNOTIFY)
 				SEND_SOUND(X, sound('sound/items/PDA/ambicha4-short.ogg'))
 	to_chat(usr, "Your prayers have been received by the gods.")