fixes botkeeper displaying wrong states (#86786)

## About The Pull Request
bot modes werent correctly reflecting the bot's AI states. this pr fixes
that. also fixes some issues where the bot's AI might get stuck
inbetween switching modes

## Why It's Good For The Game
closes #86771

## Changelog
🆑
fix: botkeeper now displays bot's correct states!
/🆑

code/modules/mob/living/basic/bots/_bots.dm

@@ -538,6 +538,7 @@ GLOBAL_LIST_INIT(command_strings, list(
 /mob/living/basic/bot/proc/bot_reset(bypass_ai_reset = FALSE)
 	SEND_SIGNAL(src, COMSIG_BOT_RESET)
 	access_card.set_access(initial_access)
+	update_bot_mode(new_mode = src::mode)
 	diag_hud_set_botstat()
 	diag_hud_set_botmode()
 	clear_path_hud()
@@ -558,8 +559,7 @@ GLOBAL_LIST_INIT(command_strings, list(
 	// process control input
 	switch(command)
 		if("patroloff")
-			bot_reset() //HOLD IT!! //OBJECTION!!
-			set_mode_flags(bot_mode_flags & ~BOT_MODE_AUTOPATROL)
+			set_patrol_off()
 		if("patrolon")
 			set_mode_flags(bot_mode_flags | BOT_MODE_AUTOPATROL)
 		if("summon")
@@ -567,6 +567,9 @@ GLOBAL_LIST_INIT(command_strings, list(
 		if("ejectpai")
 			eject_pai_remote(user)
 
+/mob/living/basic/bot/proc/set_patrol_off()
+	bot_reset()
+	set_mode_flags(bot_mode_flags & ~BOT_MODE_AUTOPATROL)
 
 /mob/living/basic/bot/proc/bot_control_message(command, user)
 	if(command == "summon")