Graduate student council programs in particular are often built as a compromise to prevent the students from forming an organization with greater efficacy.
Anecdotally, some PIs I know have had to directly contend with rising organization among students and handed out a raise and a bonus to their labs.
According to the spirit of the law, all jobs are permanent by default. Fixed-term positions require a valid reason. A project (such as completing a PhD) is a valid reason. The availability of funding is not. While an externally funded research project could be considered a project, it's reasonable to assume that someone in the university will apply for funding for similar research in the future. Because someone is planning to continue similar projects in the future, the need for that particular externally funded researcher does not end when the initial grant runs out. And even if those applications fail, the university still has other money for paying the salary. The employment should continue until the university decides to reduce the number of people doing that kind of research permanently.
In principle, it should be categorically illegal to hire fixed-term postdocs, but the academia does not work like that. Because the union is a union first and a representative of specific people only after that, it's extremely unwilling to let go of the "all jobs are permanent by default" principle. There must be a compromise that allows the international standard practice of hiring postdocs for a few years without letting the employer to chain fixed-term positions indefinitely. Whether 4 years is a good compromise is debatable, but it's easy to see why a union would want something like that.
Also, from a Finnish perspective, Sweden has a reputation as a country where it's relatively easy to get a permanent academic position.
Traditionally for better or for worse, undergraduate representation comes by way of a student council, with a single person elected to a chair on the larger university advisory council (the structure can be different depending on the university, I'm generalizing).
https://mitgsu.org/updates/we-have-an-election-date-vote-yes...
Note that for instance if you're there with a fellowship and aren't getting a partial RA/TA assignment as well then you're not eligible. I know that some masters students pay for their tuition, so they might not be eligible either since they're not getting a stipend.
https://www.inf.elte.hu/en/content/doctoral-training.t.1616?...
[0] I expect that if someone wants to do a PhD in teaching methodology they might have to still do some teaching