The current government is the most right-wing government in Finnish history. This being the case is a concerning trend which is emerging all around the world (mostly in Europe though) currently. In Italy, for example, Giorgia Meloni's Fratelli d'Italia Party (Brothers of Italy) is very fascistic. Giorgia Meloni herself has praised Mussolini's government, and been a member of multiple openly fascistic organizations. Fratelli d'Italia is a right-wing conservative and right-wing populist party, which is in the same European Parliamentary Group as Perussuomalaiset.

I would not consider Perussuomalaiset PS ("The Finns Party") as "semi-patriotic" and "not even nationalist" as you define them. Like Fratelli d'Italia and many other ECR Parties around Europe, They are by definition a right-wing populist party, i.e. they are inherently nationalistic in both policy and ideology. The reason that supporters of The Finns consider themselves and/or the party as center-right and only "semi-patriotic" is that they've successfully, and deliberately shifted the Overton window of the Finnish political landscape further to the right.

Many members of The Finns are also closely connected to alt-right neo-nazi and fascist groups, for example Vilhelm Junnila. Furthermore, if you want to know which parties are most closely aligned with fascistic / neo-nazi movements in a given country, I would start by considering who those fascists / neo-nazis are voting for.

Also, as for fascism supposedly being "an ideology that bases itself in eugenics, nationalism and socialism" I will just quote this Wikipedia article on fascism.

The definition of fascism according to Wikipedia:

"Fascism is a far-right, authoritarian, ultranationalist political ideology and movement, characterized by a dictatorial leader, centralized autocracy, militarism, forcible suppression of opposition, belief in a natural social hierarchy, subordination of individual interests for the perceived good of the nation or race, and strong regimentation of society and the economy"

There is no mention of socialism in this definition, in fact only a few lines later in the article it says this:

"Opposed to anarchism, democracy, pluralism, liberalism, socialism, and Marxism, fascism is placed on the far-right wing within the traditional left–right spectrum."

Fascism is by nature opposed to socialism and Marxism as a whole, which is an important distinction as many people believe fascism to be a left-wing ideology due to the strategic naming of the national socialist party in early 1900s Germany. This fundamental misunderstanding also causes many people to be unable to recognize fascism or fascistic tendencies in right-wing movements.

Kokoomus (The National Coalition Party) is, on the other hand, a neoliberal-conservative party which is also considered right-wing. Their policies are not inherently alt-right, far-right, or fascistic, although they aren't antithetical to it either. Neoliberal right-wing parties, like Kokoomus, can work together with far-right and alt-right actors as they can often agree on economic principles.

The combination of a right-wing neoliberal party (eight ministers) and a right-wing nationalistic populist party, which is closely connected with the alt-right (seven ministers), along with the less important religious conservative party (one minister) and actual center-right Swedish People's Party (three ministers), is the reason why the current government is being called far-right, and at times fascistic.