Sure, happy to expand.
Stepping back quite a bit, the US constitution divides up responsibilities between the Legislator (Congress), the Executive (President), and the courts (Supreme Court).
The Legislator is given rights over declaring war, applying tariffs and levying taxes, federal budget, approving international treaties, and of course writing laws. Over the past 250 years, the legislative branch has slowly given the executive branch more discretion. In times of emergency, the legislative branch moves too slowly, so the executive branch is better suited to make snap decisions.
Trump, as soon as he's taken office, immediately used these powers to declare an emergency at the border (https://www.whitehouse.gov/fact-sheets/2025/01/fact-sheet-pr...) and redirected the military to intervene. It's an abuse of the power, as the situation has been relatively stable (enough so that congress should have had time to meet and decide on next steps), but it's something he did in his last term as well (https://trumpwhitehouse.archives.gov/presidential-actions/pr...) so was expected. What wasn't expected was the repurposing of Guantanamo Bay (a military prison with a dark history outside the jurisdiction of most US courts) now being used for migrants (https://www.bbc.com/news/articles/cy0p1ykxyzjo). It's a worrying trend of moving undesirables somewhere out of sight of the general public. In his last term, there were detention centers inside of the US (https://abcnews.go.com/Politics/tornillo-texas-tent-camp-hou...) with poor conditions -- most notably, Trump pardoned one such sheriff (https://www.npr.org/2017/08/25/545282459/president-trump-par...) who was remarkably cruel and called the tent cities personal concentration camps. This shift to move migrants to more restricted areas is seen as a way to avoid oversight.
Trump likewise invoked the International Emergency Economic Powers Act to levy tariffs against Canada (https://www.whitehouse.gov/presidential-actions/2025/02/prog...), Mexico (https://www.whitehouse.gov/presidential-actions/2025/02/impo...), and China (https://www.whitehouse.gov/presidential-actions/2025/02/impo...). Again, these powers are usually invoked in response to war, so it's considered an abuse of power. Canada and Mexico are also close allies and a part of USMCA, which is a treaty promoting free trade between the three countries; Trump negotiated & signed the USMCA treaty when he was last in office, and has since called it a bad deal and these tariffs directly conflict with it. It's put the US in a situation where allies are being alienated. Trump has also threatened tariffs against the EU and Taiwan, both of which currently count on US military intervention in case of war, which is straining those relationships as well.
Republicans, hopefully more as a show of solidarity than an act they'd follow through with, have also introduced legislation (https://ogles.house.gov/media/press-releases/rep-ogles-propo...) to allow Trump (and only Trump) to run a 3rd term as president. This kind of twisting of the laws is something you'd expect more in Russia or other puppet governments and leaves a bad taste. Similarly, legislation to add Trump to our national landmarks (https://www.congress.gov/bill/119th-congress/house-bill/792) have been floated while Trump has had historically low approval ratings when compared to past presidents (https://news.gallup.com/poll/203198/presidential-approval-ra...).
In Trump's previous term, he appointed several Supreme Court justices. The court is idealistically an unbiased and independent branch, and are given lifetime appointments as such, but the political leanings of the court have shifted with these new appointments. Abortion, a controversial topic in the US, was recently made illegal in several states after the court re-ruled, on party lines, a 50-year standing (https://www.supremecourt.gov/opinions/21pdf/19-1392_6j37.pdf). More recently, and relevantly, though, the supreme court ruled again on party lines that the president cannot be taken to court over illegal acts while in office (https://www.supremecourt.gov/opinions/23pdf/23-939_e2pg.pdf) and that only congress's power of impeachment can be used. With a republican majority in both houses of congress (and impeachment requiring 2/3rds approval to convict), there seem to be little to no recourse to anything Trump has done or plans to do regardless of legality. It's democratic in a sense -- the US population voted for a majority in the house and senate and so we're getting what we voted for -- but there's 2 years until the next election, so there's a prevailing sense of helplessness.
Getting into powers of the purse, as mentioned before, the executive branch is expected to dutifully carry out the budget and laws set by the legislative branch. This includes the creation and running of departments, as well as getting senate approval for department heads. Notably, Elon Musk is not a senate-approved department head, but he's been given dangerous amounts of access to the treasury (https://www.wired.com/story/treasury-department-doge-marko-e...) and other departments. This is without going through the normal vetting process (although, as President, Trump does have the power to bypass such requirements. It's simply against norms, and raises concerns about the possibility of blackmail, espionage, and hacking). Elon has also declared several departments as 'criminal organizations' (https://www.npr.org/2025/02/03/nx-s1-5285539/doge-musk-usaid...), Trump has fired anyone who has pushed back against Elon's requests, and funding for most departments has been paused pending review. Trump has also offered almost federal employees a Voluntary Exit Program (VEP) (https://www.opm.gov/fork/), although the legality of such a VEP is debated since past court cases (https://www.oyez.org/cases/1989/88-1943) have ruled that congressional approval is necessary. If that's the case, anyone who resigns may not end up being paid. This is seen as a wider purge (eg. https://apnews.com/article/trump-fbi-firing-a7b19a5f414ce82c..., https://www.cbsnews.com/news/trump-federal-inspectors-genera...) of the government to replace federal employees with loyalists to the president (instead of to the constitution).
And for Elon specifically, during Trump's inauguration he did his infamous "My heart goes out to you" salute (https://www.youtube.com/watch?v=-VfYjPzj1Xw) which is seen as a poor attempt to signal to the far right and neo-nazi parties, that typically have supported the republican party, that they are welcome and in positions of power now. Elon also spoke at far-right rallies in Germany (https://www.reuters.com/world/europe/elon-musk-appears-video...) championing lines of nationalist empowerment. At face value, it's innocent enough, but these terms are also seen as a dogwhistle for neo-nazis and so it's seen together as another vocalization of support for them.
Trump also pardoned everyone involved in the insurrection on January 6th, who had invaded the capital and attempted to abduct the congressmen and vice president to stop them from ratifying the peaceful transfer of power in 2020. This is seen as a nod from Trump that if you support him, you will have immunity for your actions.
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The US populace voted for this, so if it's a coup it's a bloodless one. But everything Trump has done in the few weeks he's been in office is very extreme by the standards of the US. The transfer is power is usually peaceful, and builds upon the work of past presidents. This is a very abrupt departure from that, and no concern is given to impressions of corruption and nepotism.