> So in general the EU freedom of movement is "freedom of movement of workers", not just anyone.
Exactly. For Americans (and other) readers there are four freedoms in the single EU market: free movement of goods, capital, services, and workers, known collectively as the "four freedoms".
People and workers may/are often used interchangeably but in laws it is about worker's freedom to move between borders, not people.
I think it's an interesting difference with the united states which is older than the EU but younger than Europe. It also highlights that in law, in modern Europe, capital goods, services and workers have rights to cross borders while the US American citizens are free to cross state borders.
Strangely those laws are all about workers and the market but nevertheless and contrary to the US most EU countries still have a much better social security net (for people) than "neoliberalcapitalisticmoneyhungryonly" US which has freedom at its core.
https://en.wikipedia.org/wiki/European_Single_Market#People
> Since its foundation, the Treaties sought to enable people to pursue their life goals in any country through free movement.[122] Reflecting the economic nature of the project, the European Community originally focused upon free movement of workers: as a "factor of production".[123] However, from the 1970s, this focus shifted towards developing a more "social" Europe.[124] Free movement was increasingly based on "citizenship", so that people had rights to empower them to become economically and socially active, rather than economic activity being a precondition for rights. This means the basic "worker" rights in TFEU article 45 function as a specific expression of the general rights of citizens in TFEU articles 18 to 21. According to the Court of Justice, a "worker" is anybody who is economically active, which includes everyone in an employment relationship, "under the direction of another person" for "remuneration".[125] A job, however, need not be paid in money for someone to be protected as a worker. For example, in Steymann v Staatssecretaris van Justitie, a German man claimed the right to residence in the Netherlands, while he volunteered plumbing and household duties in the Bhagwan community, which provided for everyone's material needs irrespective of their contributions.[126] The Court of Justice held that Mr Steymann was entitled to stay, so long as there was at least an "indirect quid pro quo" for the work he did. Having "worker" status means protection against all forms of discrimination by governments, and employers, in access to employment, tax, and social security rights. By contrast a citizen, who is "any person having the nationality of a Member State" (TFEU article 20(1)), has rights to seek work, vote in local and European elections, but more restricted rights to claim social security.[127] In practice, free movement has become politically contentious as nationalist political parties appear to have utilised concerns about immigrants taking jobs and benefits.