Function overloads condensation (#18939)

Unified most of the procs into one definition, so there are no duplicate
around the codebase.
Marked some of the above as overridable if a good enough case can be
made for them (eg. external dependency or unlikely to be used).

code/modules/tgui_input/say_modal/typing.dm

@@ -18,15 +18,6 @@
 /mob/proc/remove_all_indicators()
 	return
 
-/mob/set_stat(new_stat)
-	. = ..()
-	if(.)
-		remove_all_indicators()
-
-/mob/Logout()
-	remove_all_indicators()
-	return ..()
-
 /** Sets the mob as "thinking" - with indicator and variable thinking_IC */
 /datum/tgui_say/proc/start_thinking()
 	if(!window_open || (client.prefs.toggles & HIDE_TYPING_INDICATOR))