[LuaDoc] Fix several minor errors in the specification of API

data/lua/core/_initial.lua

@@ -11,7 +11,7 @@ local _ = wesnoth.textdomain "wesnoth"
 ---@param elem_name string the full name of the element being deprecated (including the module), to be shown in the deprecation message
 ---@param replacement_name string the name of the element that will replace it (including the module), to be shown in the deprecation message
 --- Can be nil if there is not replacement, though this should be an unlikely situation
----@param level '1'|'2'|'3'|'4' deprecation level (1-4)
+---@param level 1|2|3|4 deprecation level (1-4)
 ---@param version string|nil the version at which the element may be removed (level 2 or 3 only)
 --- Set to nil if deprecation level is 1 or 4
 --- Will be shown in the deprecation message

data/lua/core/mathx.lua

@@ -90,7 +90,7 @@ end
 
 ---Randomize the order of an array
 ---@param t any[]
----@param random_func fun(a:number,b:number):number
+---@param random_func? fun(a:number,b:number):number
 function mathx.shuffle(t, random_func)
 	random_func = random_func or mathx.random
 	-- since tables are passed by reference, this is an in-place shuffle

data/lua/core/wml.lua

@@ -62,6 +62,7 @@ end
 ---@param name? string Tag to search for.
 ---@param filter WML A WML filter to match against
 ---@return WML? #The WML table of the child tag
+---@return integer? #The overall index of the child tag
 function wml.find_child(cfg, name, filter)
 	ensure_config(cfg)
 	if filter == nil then

utils/emmylua/wesnoth.lua

@@ -10,6 +10,10 @@ function wesnoth.kernel_type() end
 function wesnoth.dofile(path, ...) end
 
 ---@class tstring : string
+tstring = {}
+
+tstring.format = string.format
+tstring.vformat = stringx.vformat
 
 ---Constructs a textdomain, which can be called to create translatable strings.
 ---@param domain string The textdomain name
@@ -119,7 +123,7 @@ function wesnoth.ms_since_init() end
 
 ---Output a deprecated message
 ---@param element_name string The name of the element being deprecated
----@param level '1'|'2'|'3'|'4' The deprecation level
+---@param level 1|2|3|4 The deprecation level
 ---@param version string|nil The earliest version the element may be removed in
 ---@param detail_message string An additional message describing the deprecation and usually indicating a replacement
 function wesnoth.deprecated_message(element_name, level, version, detail_message) end