From your question, I don't see anything that you are doing wrong. If there is a problem as you describe it, then the problem is more likely with the survey papers you are reading than with you.
these papers just outline briefly each methods without going deep enough
By definition, that is what a "survey" paper is: it gives a broad survey of a topic, not a deep-dive into any specific aspect of the topic. However, a survey paper cites relevant references so that a reader like you knows where to go to dive deeper into any specific surveyed topic.
I'm still left with A LOT of question marks about why certain method is used, why certain modifications are necessaries, and how particular approach works in details
This is entirely a matter of the quality of the survey paper. A high-quality survey paper should not only list what has been done, but it should answer the why questions that you are looking for.
If you find the only survey papers that are published to be unsatisfactory for answering the most important questions, then there is not much to be done other than hope that an expert will write a high-quality survey. Otherwise, you might consider this as an opportunity for research so that later on, when you build sufficient expertise, you might write that survey paper that you wish had been available to you.
An intermediary solution might be to contact an editor of a highly reputable journal in the field and suggest that they invite a senior expert to write an appropriate review (you could propose some experts based on the most highly cited papers in the survey). Editors often appreciate such pointers because they want to publish articles that will get widely read, so an editor could take your unsolicited suggestion very seriously.