My thoughts have been that the main linguistic effect of continued Swedish rule of Finland, would mainly be that northern Finland turn Swedish speaking (thanks to it being settled in a similar manner to northern Sweden and Norway in the 19th century. Helsinki stay a less important town (200k people by modern day) thanks to it not becoming the Finnish capital but stay Swedish speaking, this also keep the southern coast as coherent Swedish speaking region. Vaasa stay completely Swedish speaking. Turku end up an either a 50/50 bilingual city or end up the Brussel of Finland (Swedish speaking with a mostly Finnish hinterland), Turku also end up the major city of Finland (around one million people). Beside that I expect the linguistic borders to stay mostly the same, but the number of Swedish speakers will be significant bigger just with these small changes.
Political I expect the linguistic strife to be just as ugly or uglier than in OTL, and the Finns to have a strong independence movement. But in the end the fact that Sweden are richer than Finland and Sweden would obvious cut out the Swedish coastal exclaves in case of independence will likely keep the independence movement peaceful and as a minority.
I'll add my stock comment, that not only would the eastern provinces be more Swedish than IOTL, Sweden in general would be significantly more Finnish than it has been after 1809 IOTL. Many comments on Sweden retaining Finland tend to emphasise just the differences east of the Sea of Åland, while the fact that one third of the realm being Finnish-speaking, and otherwise culturally, etc, Finnish would have major knock-on effects for Sweden at large rarely seems to come up. Just imagine how many more politicians, soldiers, bureaucrats, artists and professionals of different stripes this bigger Sweden would have that Sweden didn't have IOTL, and what kind of an effect this would have. Many of these people would come from families where Finnish is the first language, and many would have a distinct "Finnish" identity (even if that identity would be different from IOTL). The comparative number of Finnish speakers having a voice in the realm would also increase through the 19th century, with the growth of a Finnish linguistic and cultural identity, and the spread of better education also in the eastern part of Sweden. While the main language of the realm would be Swedish, the eastern part of the realm would stay at least 70-80% Finnish speaking, and "Sweden proper" would also possibly have a bigger Finnish speaking minority than Finland has a Swedish speaking minority today, say 10% or so.
As for northern Finland becoming more majority Swedish speaking, I don't know if that is at all a foregone conclusion. While Stockholm would like to populate Lapland more to better utilise it economically, it is the Finnish speakers that have a history and tradition of being settlers of new lands in the realm. Populating Lapland with Finns might need smaller economic incentives than using comparatively more affluent Swedish speaking population for that effort.
Turku/Åbo would be the biggest town in the eastern part of the realm, and one high up among the hierarchy of the country in general, an important centre of the economy and of governance and learning. The university there would likely be among the top three in the country, given its catchment area would be one third of the realm. Population-wise, Turku/Åbo could stay 50/50 Swedish and Finnish well into the 19th century, but generally speaking it would see its growth coming from mainly Finnish speaking areas. It would thus transform into a clearly majority Finnish speaking city by the end of the century. Otherwise, any major centres in the interior of Finland would be obviously Finnish speaking in the main. The internal structure of this Swedish Finland, and which towns rise up in prominence, would be dependent on many things, say on the placement of the railways when they arrive. Like has been discussed in previous threads on the subject.