It’s so hard!
My only puppy was before crating became normal in the U.K. so he just had a bed in the dining kitchen in a very small two up two down cottage. Like you I slept downstairs on the sofa and he was in the neighbouring kitchen with a lino floor until he was sleeping through as he was a giant breed and we had a steep kite-winder staircase that he couldn’t have used safely so him sleeping upstairs was never an option.
Are you a light sleeper? I found because he was on my mind, like when my babies were tiny, I’d wake up as soon as he started stirring and I’d be up and out in the garden with him before he got round to weeing or pooing. If you are a heavy sleeper a monitor might help. I was always silent and boring in the night except for very muted praise once he’d done a wee or poo. He was on a loose lead at night in the garden and I had a torch so I knew if he was going or not. It was February and we had snow and it was fucking freezing! During the day I took him out on waking from naps, after playing, after eating or every 30 mins. I think he was on a loose lead then too but can’t swear to it. The door wasn’t left open because the weather was freezing but I think that also helped toilet training because I knew when he had and hadn’t toileted and he also learned very quickly that the garden was for weeing and pooing.
During the day you could do the flitting game, never preventing him from following you, but hopefully boring him and reassuring him into relaxing in the knowledge that you leaving him doesn’t mean abandonment. Unfortunately because the crate door was shut overnight that will have created anxiety so I wouldn’t consider shutting that door again in the near future.
If you lift all rugs and maybe buy a big piece of a cheap roll of vinyl flooring to cover most of any carpet, you can minimise the work and stress of inevitable accidents. I’m sure you know this but it’s important not to make a fuss of accidents as that just creates more anxiety around toileting.
My puppy was from a breed that although very devoted, is a more independent and steady breed than many companion or sporting breeds so I realise I might have had an easier ride than is normal for puppies. He wasn’t a Velcro dog but on the other hand he was never physically prevented him joining us if he wanted to. Dear god the mouthing though! My forearms were covered in bruises for weeks.
At 3 days your puppy is so tiny it’s fine for him to be with one of you all the time, even if that involves him following you to the loo. Is there a loo you can use that he can follow you too if he wants to? I’d leave doors open and not announce your plans but crack on and let him join you or not. If he follows ignore him, you want to be quite boring some of the time so eventually he’d rather not get up, or break off chewing on that nice toy every time you move out of sight.
It’s such early days. This won’t be the rest of your life, I promise!