History master student from Fu-jen Catholic University (Taiwan) here, studying the ideas of Joseph de Maistre (1753-1821, conservative Catholic thinker).
Cultivated fields, such as intellectual history of the Enlightenment and the French Revolution, are already dotted with classical researches. Even with Hermione's time machine one can hardly finish reading even the most important ones among them.
In my own experience, I spend quite some time on the metadata of books and articles I find, assessing their academic quality, factuality of first hand sources, translation quality, pertinence (whether it interests me and whether it relates to my knowledge pool), and readability (grammar not unnecessarily difficult, acceptable volume, good citation format...). The side effect, however, is that I spend too much time on these metadata and not enough time on reading (or: too much energy/time spent on context and no time for text).
I still believe that very few historical fields are "too crowded," as new perspectives and new questions come with future generations. But how do experienced historians prevent themselves from drowning in too many previous researches?
And, in the worst case, if I make an honest mistake (in my master thesis at very least) by claiming an independent discovery without knowing about a previous work which said the same thing, am I plagiarizing? Even if not, isn't it rather fruitless to "reinvent the wheel?"
Everyone has their own lines they are willing or interested in drawing in how much time they spend engaging with past or even current secondary sources. You are under no obligation to know everything that has been written on a given topic, nor to even engage with it. But there is an expectation you will know the "standard references" (e.g., the main secondary sources that probably most articles or books on the subject published today would reference) and that for any sub-topic you will do some real due diligence to make sure you are not missing something important or vital.
When you start out, in graduate school, you are just going to drown in this stuff — or at least, try to learn to swim in it. That's sort of what grad school in History is: an initial flailing that, over the course of it, starts to look like swimming. You can't get around that; it's inevitable, and it's necessary. It's what happens even later in a career if one suddenly tries to shift into a different area of focus, you once again have to jump on in and hope you come out the other side OK.
One of the positive things about historical research is that it is to some degree additive, so over the course of a career one gets more and more familiar with more and more writings and gets more and more insights and perspectives and facts to draw upon. So it starts to look very easy, because you've already done the drowning/swimming you've mentioned, and don't need to do as much of it. So if I want to work on a topic that is part of the shared corpus of what I have already worked on, I can really just jump into it very quickly and not worry about missing too much. And it looks rather effortless on the outside, because you can't see the ~20 years of work it took to get to this point.
It is totally the case that people decide that they don't want to work in a field because it is too crowded, too over-grown, or because they learn that someone who they think is very good has just pivoted to that field and they don't want to feel like they are competing. It's up to you what you do and the reasons for which you want to do it; the entire goal here is research autonomy, that you are in charge of it. So you should not feel beholden to any grand sense of what you "should" do. Do what you want to do, and you'll both be happier as well as more successful as a researcher and writer (because nothing is as motivating as genuine enthusiasm), and don't worry about what other people think (they truly are not spending that much time thinking about you and your choices anyway).
In terms of your "honest mistake" idea — it's not plagiarism if you came up with it independently and unaware that someone else already came up with it. There's no true misrepresentation there (just error), and misrepresentation is the heart of plagiarism. So don't stress about it too much. As for whether it is fruitless or not, I have tended to find that no two scholars ever truly have the exact same idea. They can have similar ideas, and they can come to similar conclusions, but their way of getting there is usually different, their specifics are usually different, and ultimately the experiences that lead them to those places are different. So even two people arguing very similar things tend to do it somewhat differently. Is it ideal for your career to "reinvent the wheel"? Obviously it would be better if you were the first inventor. But is it some kind of moral or intellectual failing? Not really — even if you did completely independently rediscover the exact same thing, at its worst it just sort of shows that this idea was a pretty compelling one, since multiple people took multiple paths to it. The only way it is a failing is if you really ought to have already stumbled across the idea/discovery in the course of your research (like, it would be surprising for you not to, because it was a well-known thesis or a well-known document or whatever), and you didn't because you didn't do due diligence. But again, there is no "hard and fast" rule for what constitutes enough due diligence.
The best way to avoid these kinds of situations, other than doing a lot of drowning/swimming, is to show your work to more senior people in your field (at conferences, in drafts, in journals), because these people are the ones who have been drowning/swimming longer than you, and if it is something quite reasonable to know, they'll know it. If neither you, your advisors, your colleagues, your journal referees, your journal editors, etc., know something, then it does reflect poorly on you as an individual; it means it is just quite obscure by its nature!