Before the age of nationalism, Finns were Swedish subjects, which meant they paid taxes to the King of Sweden, served in the Swedish army, and so on.
The hallmarks of civilization at the time – Christianity, writing, organized armies, etc. – were closely associated with Swedish rule in Finland.
A map showing some of the areas that were temporarily under Swedish rule after the conquest of Finland – what was actually ruled was a different matter
But this applies mainly to the coastal areas (and to some extent to Tavastria). Outside of these areas, Finland is basically Finnish, where Finnish-speaking people have lived for thousands of years.
The Swedish crown was primarily interested in economic and military matters, and was less concerned with nationalistic assimilation efforts, so there was no real effort to turn Finns into Swedes.
As long as the Finns paid their taxes and provided good soldiers, the Swedish crown was happy. If they wanted to advance in the army or in the church, then they had to learn Swedish.
Having said that, people have been moving back and forth across the Baltic Sea for centuries, through assimilation, and modern genetic testing has proven this fact (my daughter has Finnish blood on her mother’s side, probably going back a century), so in Sweden people make Finns into Swedes by having children, and vice versa.
However, language and culture are not passed on genetically; Finnish and Swedish are similar to Chinese and Korean. Except for loanwords, Finnish has no real similarity to Swedish, just as Danish is close to Swedish in my home country of Scania.
When nationalism and anti-imperialism emerged, the Finns were Russian subjects and therefore no longer a problem for the Swedish authorities.
Swedish is taught in Finland as part of the school curriculum, but with the declining importance of Sweden in the global environment and the increasing importance of English, it is a dying practice that is basically only retained for historical reasons.