The first ten amendments (collectively, the Bill of Rights) were written and passed specifically because the lack of guarantees of civil rights was called out during debates of ratification, and a few states only agreed to ratification with the understanding that a Bill of Rights would be passed. Beyond those amendments, several more amendments also aimed specifically to identify more civil rights that needed constitutional guarantees of preservation; it's actually shocking how few amendments are geared towards altering the structure of government itself.
Some of the amendments, particularly the first ten, deal with more philosophical matters such as rights retained by the people which the government could not abrogate, or other checks on government power. If a person has a grievance against the government in the United States, generally it would be litigated under the auspices of the first ten amendments or the fourteenth amendment.
Significant portions of the main body, such as the election of senators by state legislatures and the "three-fifths" clause (according to which three fifths of the total number of slaves in a state were counted for purposes of allocating representatives to the House of Representatives for that state) were nullified or superseded by amendments.
To understand our love for the first 10 (the bill of rights), you have to understand the context in which they came into being. The US constitution was a positive document, written to grant powers to the US federal government with the implied understanding that all powers not granted to the federal government were reserved for the states or for the people.
Immediately after ratification, the Federalists began to push for more and more powers for the federal government. The constitution's positive nature had a major flaw--it assumed a good faith understanding that the federal government should be as limited as possible, and that unstated powers were necessarily beyond the intended scope of the government. In the absence of that good-faith understanding, the powers of the federal government could (if only in bad faith) interpret the powers of the federal government quite broadly.
To rectify this problem, the first ten amendments (collectively known as the "Bill of Rights") were passed. These are 'negative' in nature, in that they explicitly lay out things which the government cannot do. The nature of the constitution as a generally 'positive' document, where things not listed are not to be assumed to be powers of the government, which was only implied before the bill of rights, was formalized in the 10th amendment.
The rest of the amendments are kind of a grab-bag. To understand why we focus on them, consider that the original constitution is only ~4,500 words long! And from that short document, all constitutional questions were to be answered! These questions are generally answered by the US Supreme Court's 'interpretation' of the constitution, including amendments and its own case law. Generally, amending the constitution is a for the people to decide specific constitutional questions for themselves, rather than relying on SCOTUS to extrapolate from a small body of black-letter law and case law.
The fact that there is more focus on these amendments is, when you think about it, almost tautological. If a constitutional question really matters, we can take it into our own hands and answer it via constitutional amendment. If it doesn't matter all that much (or we can't agree enough to pass a constitutional amendment), we have to rely on SCOTUS to answer the question.
the bill of rights (the first ten amendments) describe what the government can’t do
because the government frequently tries to violate the first ten amendments you hear about some of them a lot, and the people feel they have to make it their whole identity to defend some of those rights
The constitution lists some things the government can't do, like "no Attainder of Treason shall work Corruption of Blood, or Forfeiture except during the Life of the Person attainted" and "The Citizens of each State shall be entitled to all Privileges and Immunities of Citizens in the several States" means the government may not privilege the citizens of one state over another.
The latter is called the "Privileges and Immunities Clause", and there are court cases dealing with it. https://en.wikipedia.org/wiki/Privileges_and_Immunities_Clau...
Definitely more court cases than for the Third Amendment (quartering soldiers in private homes), where even this link had to stretch to find a relevant movie.
As another example of a restriction on government in the main body of the Constitution, Article I, Section 9, Clause 1 said the government could not pass a law prohibiting the importation of slaves 1808 nor set a tax or duty of more than $10 on those slaves.
Even the "frequently tries to violate the first ten amendments" characterization suffers from some built-in bias error as there are far fewer entities that can sue over, say, the Supremacy Clause than the First Amendment, and something like Medellín v. Texas is more a "nuclear power plant" than a "bicycle shed", in the classic story of the law of triviality.
That's likely why our foreign companion has not come across anyone online talking about the lawsuits over the various clauses in the Constitution proper.