one other thing is that when you see advice to check the sources of claims it can be a bit overwhelming. if you're reading a 400 page book how are you supposed to check the soundness of every singular sentence in the book through the hundreds of texts in the bibliography - both in their facts and in their analysis - and then the soundness of their sources too? obviously there is no point at which you will instinctively know whether a new statement is true or not. but the more you read, the more you learn that whenever you encounter a new statement or something you want to integrate into your knowledge, you should watch out for:
general statements: is it a "(people) have been doing (x) for centuries" type statement, that is necessarily a broad generalization? could such a statement possibly be true about various locations or decades? if its a statement about a country, could it apply across class, geographic, national, linguistic, or religious lines? does it presuppose a state unity that existed prior to the formation of the nation state, or even fully after it?
anecdote: is it an anecdote being recounted in one person's letters or autobiography? is it posthumous? are there other corroborations of this event occurring in those terms? can you find other sources on this event?
idealism: what version of history is this statement highlighting? is it a "great man of history" version? is it using a supposed "national character" to explain political developments? is it explaining state decisions through individual actors' feelings and commitments?
exceptionialism: if something is being presented as a contemporary development, especially if it's a negative one, what figures is this statement based on? is it presenting modernity as a break with a timeless tradition? are things really "as they've never been before"? is it presenting a nuanced understanding of past and present, continuity and rupture, or is the past painted in broad strokes without the attention given to the present?
primary sourcing: did the author base their analysis on other people's analyses or comments? if they are, for example, talking about the state of a city in a certain year, are they going through municipal archives or only relying on subjective testimonies? if they rely on subjective testimonies, are they highlighting the fact that this is a subjective perception or treating it as an objective assessment?
metatext: what in the sources would need to be true for this claim to be correct? if a claim is being made about an identity, how does the author define the boundaries of this identity and the relationship of the claim to this identity (correlation, cause, consequence)? if the source is a medical or social study, is this study (or sometimes, is any study) capable of proving or disproving the claim being made? what assumptions does this claim being correct or incorrect rest on?
unless you are researching a specific paper, it is unlikely you will truly be checking every single source in every singular bibliography of every book you're reading, but these tips can help you sharpen your critical sense towards new statements you encounter