I imagine its the same everywhere or at the very least in Europe. Short answer: yes, you will go to a psych ward for attempted suicide.
If you end up in a hospital and the cause is self harm, especially attempted suicide, you will 100% get sent to a psych ward under the supervision of a psychiatry board from which one will be assigned to you.
Your parents or closest relatives will be called if they werent already there.
The psychiatry board will then call you in to talk to you to gather information on what "treatment plan" would best suit you and check your mental state. And yes, its just as bullshit as it sounds, but everything is up to them at this point as youre deemed dangerous and a threat to others or yourself.
From my experience you are given whatever pills they deem necessary everyday, 3 times a day, in the morning, at lunch and before going to bed and the nurses do watch you take them and yes, you have to open your mouth and move your tongue too so you cant pretend to swallow the pills. (at least where I was)
Then every other day the psychiatrist comes to talk to you about how you`re doing, in which case I personally just answered whatever they wanted to hear. Dont think for a moment they give a shit, because if you speak your heart out you will just prolong your stay and be given more pills.
I also got benzo something (forgot the name) to make me sleep and whatever else they gave me like injections for panic/anxiety attacks and more pills. I dont remember everything so well from my stay there, its all foggy.
Also you get to stay in a room with 2-3 other people.
You will be released whenever the psychiatrist deems so and even if they do, you will then be checked by the full psychiatrist board for evaluation.
Its just disgusting we still have psych wards at all, given how dehumanizing and pointless they are.