It is extremely capitalist with classical hierarchies of business ownership. High tax, free healthcare and free schooling does not make a country even remotely socialist.
The whole point of reformist socialism is that you should not try to get there in a single giant leap, but step by step, with the fully socialist society more of a Platonic ideal: There'll likely always be a next thing to fix.
Austria having free education does not make it socialist - but it makes it more socialist.
Similarily for capitalism-socialism. It is a spectrum. The United States represents one extreme, where something like, I don't know, North Korea maybe represents the other. And Finland is somewhere in-between.
Take, for example, a country where the majority of things are privately run but are heavily taxed by the government. Is that more capitalist or socialist than a country where most of the economy is run by the government, but the remaining private businesses pay little to no taxes?
Or a country where one party owns everything but pretends to act on behalf of the workers, as opposed to a country where everyone is a business owner? Or a country that has little labor regulation but a strong social safety net, versus a country with weak social welfare but strict labor regulation?
If Bernie Sanders had his way[1] and this was implemented in the US, the country would become more socialist.
[1] https://berniesanders.com/issues/corporate-accountability-an...