The detection system isn't broken, but it's definitely finicky on Switch - and there are a few things that trip people up.
First, the closed eye icon doesn't mean you're totally safe. It just means you're not currently detected. The second you draw your bow, you're committing to an action, and guards can spot the animation even if they couldn't see you crouched. Line of sight is real in this game, but the detection radius when you're actively doing something (drawing, attacking, moving fast) is way bigger than when you're just standing still.
What actually helps: grab the perk that makes your shots silent - I think it's called Quiet Casting but for archery, or maybe it's just part of the Assassin's line? Either way, there's a perk that suppresses the sound of your shots so guards don't hear the twang. That's huge. Also, the perk that lets you move faster while crouched (something like Shadowstrike or Wind Walker in the Light Armor tree) keeps you from lingering in bad positions.
Positioning-wise, try staying further back than you think you need to. Pillars are decent cover but they don't block line of sight as well as you'd expect. Rooftops and balconies are way safer because guards rarely look up. And if you're on your second playthrough, you probably know this already, but distance = safety in stealth. Your bow has range; use it.
Are you using a silencer mod on PC, or is this pure vanilla Switch? That'd help me give better advice on what's realistic to expect.
