How detailed should PhD proposal component of a PhD application be? Some of the PhD positions I'm applying for (all in Europe, mostly UK, Germany, and Switzerland), require a research proposal as a mandatory part of the application. I'm confused about what exactly they are asking for because the guidelines are quite vague. 

I've seen this question and this one, but there are two things that are different in my case: First, the proposal for some of these programs is actually a mandatory requirement for the formal application (not for the first contact with the potential advisor), and second, unlike the former of those two questions, my field is mathematical and computational science, not Social Science (not sure if that makes a significant difference). I've also seen this question, but the question and the answers are not about how detailed the proposal should be.

My broader research interests, including a somewhat narrow area of interest for my PhD thesis (but not as narrow as a research topic), are already stated in both my statement letter (for formal application) and my contact with the potential advisor. That makes me think the proposal they expect to receive shouldn't be just my research interests, at least for those programs where, according to the guideline, it is recommended to cite related literature in my proposal. On the other hand, I really can't state a question that would be a suitable driving question for a PhD project on my own without enough help from a professor at this stage, and even if I could, I highly doubt that would be something my prospective advisor would want me to work on. So, it seems to me that writing a proper research proposal, without a substantial contribution from the advisor is impractical. (In fact, I can't even imagine how I could write about "the methodology" at this stage, considering finding the appropriate methodology in this field is often actually a very substantial part of the project.)

I'd appreciate if you could share your knowledge and experience about writing a PhD proposal as a part of the application. It would be very helpful to know what admission committees expect to see in a research proposal at the application stage, and how broad could the proposal be without turning into an SOP.
Yes indeed, I think it is expected that you would first contact the prospective advisor more informally and at minimum get an idea about the potential topics they would be interested in and that would fit with their existing research and the plans they have for the future. It's nearly impossible to guess this as an outsider.

In my case, in Germany and in CS, I had to write this for applying to the funding rather than the PhD position per se (which can be given out with almost no process by the prof). I first sat down with the prof and we talked things over and he agreed to take me on if I could acquire funding. Together with my prospective advisor and the post-doc who would be supervising me on the daily, I then wrote about 10 pages, with a detailed plan of the work I would be doing, including a gantt chart of tasks etc. Definitely not the kind of thing I would've been able to produce on my own.

I also went partway through an application process for a British university, where I had two skype interviews with the prof discussing his research before he told me to sit down and write a draft for the research plan for the formal application and send it to him for comments before submitting. (I ended up accepting another offer before I finished the draft, so I don't know what precisely they would have been looking for there.)