Are we making a mistake with the potty training? Peeing on diapers debate.

My husband and I adopted a puppy 2.5 weeks ago. We dont know her parents or exact birthdate, but we calculate she is 17 weeks by now and that she is kind of a mix of a Dutch Shepherd. She is great and intelligent, she loves the training sessions and in these 2 weeks she sits and lays down on command. I work with her every day with other basic commands and she can really focus. She is not fully vaccinated so she cannot have walks yet.

The issue is with potty training. Right now we live on an appartment with our own roof garden, and we set a big space with fake grass for the dogs to go potty there. The stairs are inside the appartment and we always have the door open. The adult dog understood the assignment immediately. She goes upstairs whenever she needs it.

But I don't know how to train Puppy. We take her upstairs to the grass every 2 hours after waking up and we train on the non-grass area during the day. She sometimes goes potty when we are there. But there is a section on the living room where she had a bed, and she started peeing and pooping on there. Our instant solution, so we dont need to wash the bed every single time, was to move it and put diapers for her on that specific spot. It worked (hurray?) Because she pees on the diapers now and we just replace it when needed. The issue is that she keeps going to the diapers when we are not watching, she does not give us notice so we can take her up nor she goes on her own upstairs to pee. For poop, she makes the effort even during the night. We know that she understands it is her bathroom. There has been 2 or 3 times where she is playing while we watch TV, then stops, goes immediately to the diapers to poop, then keep playing, by the moment we look at her and get up of the couch she is already finished. We understand, when you gotta go you gotta go. But the peeing. She doesn't go upstairs alone just to pee. We have a another balcony on the bedroom that if we keep open, she prefers to go there (A+ for the effort of doing her business outside). We cannot let her pee there because the downstairs neighbors complain about the pee that drips.

My questions are:

1. Are we unconsciously training her to pee on the diapers spot?
2. My husband and I have a debate. The diapers pads are big, so her pee doesn't cover all of it, average it would take 4 pees to fill one of them. My husband says that we should not dispose them at the first pee, let it have at least 2 times before changing it (depending on how filled it is), and also because of our experience, dogs do not like to go potty on an already filthy area it will make her to eventually go upstairs. I say that keeping the pee there will make her associate the place more with a bathroom, so I want to take them away immediately when she pees, or even so, not have them there and clean whenever she goes (the smell is not a factor here). Which of us is right?

Extra details that I don't know if matters:

1. We know our adult dog is not going on the diapers. The quantity of the pee is a LOT different between a puppy and a big dog.
2. We adopted our adult dog when she was 2 years old, so she was already kinda potty trained. We didn't go through this with her.
3. We adopted her from a government shelter, and they operated on her at 3 months removing her reproductive system. This was before us. Our vet says that incontinence may be a secondary effect. We think that is one of the reasons she pees too much.