I understand that socialising things is a strategy socialism will use to reach its goals.
Then you misunderstand.
Socialism (as per the definition that you yourself provided) advocates collective or governmental ownership and administration of the means of production and distribution of goods. When the government provides a service (like say firefighters) the goals of socialism are met by providing that social program.
You are equating 'socialist' with 'communist'. That's like equating 'capitalist' with 'monopolist'. Although they have some similarities, there are significant differences between the meanings.
No, I do not misunderstand. You are ignoring what I am saying.
The core of socialism, the political and economic idea, is not that the fire department (or health care) is state owned. Social ownership of the means of production is way more than the government providing some services (or making some insurance mandatory).
Using the same word for Socialism and the fact that the state is paying the firefighter is creating a false dichotomy.
In German, we use different words. We have a "social market economy" not "socialist market economy". We have a "Federal Ministry for Labour and Social Affairs", not a "Federal Ministry for Labour and Socialist Agendas".
So the fire department is not socialism (for me), it's a public service. Branding it as socialism
a) helps the far-right to call everyone with ideas for something like a "social market economy" a socialist, the enemies of America
b) helps the far-left to sell their ideas, because the only chance for worker rights and health care is socialism.
Sounds like it's dividing the nation, fits well into this time.
The following article seems to be interesting, though I didn't had time to read it all:
https://www.brookings.edu/blog/fixgov/2019/05/13/socialism-a-short-primer/