The position of the Finnish language in Sweden IOTL after 1809 can't be directly taken as a model for the position of the the Finnish language in this Swedish realm - on either side of the Gulf of Bothnia. Remember that Finnish-speakers would make up 25-30% of the entire population of the realm. That is, comparatively, more than there are French-speakers in Switzerland. TTL's Riksdag would see an actual, growing "Finnish lobby", in both "Finländare" and "Finne" sense. Due to this, we need to accept the idea that Finnish-speakers would have much bigger political say in Sweden past 1809 than IOTL, where the number of Finnish-speakers was much smaller within Sweden's OTL modern borders.
While IOTL Finnish is by the 21st century moribund as a language in Sweden, ITTL the situation would be different due to replenishment based on the constant movement of people across the sea. Finnish would be a major national minority language. The result is a livelier Finnish-speaking society and culture in western Sweden as well. When Finnish schools will be pushed for the Eastern part of the nation after the 1850s, say, and especially in the 20th century, they will also be pushed for those western parts of the nation where Finnish-speakers make up a significant proportion of the people.
The Flemish was a majority in Belgium from day one, it didn't really lead to favoured treatment of their language, and thjat was in a far more democratic state than Sweden. I expect the Swedish debate will be split between the "Lär Svenska din hund" faction and the "Finnish should be co-official east of th Bothnian Bay" faction.