If Karl Johan had been more secure of power in Sweden, and not feared to be murdered like the previous crownprince and the next-to-last king, or deposed like the last king, we could have had a different scenario playing out. OTL he was nice to the Norwegians so he could retreat to Norway if Sweden was lost.
Say instead that the Swedish campaign in Norway is completed, and all military resistance is crushed. Norway then becomes fully integrated into the Swedish administrative system without any special reservations.
Sweden has a new and fairly modern constitution with a strong parliament, which means that the upper crust of the Norwegian population will be able to have some influence on the future political decisions.
There was no Norwegian standard language at this time. Rural people spoke country dialects, while urban people spoke a norwegianised Danish. OTL these two modes of speech became the basis for Ivar Aasen's and Knud Knudsen's ambitions of creating the Norwegian language. ATL we instead force Swedish upon the Norwegians, and the differences are not that huge to begin with, and as the basic school system develops everyone is trained in Standard Swedish. Since there is no Norwegian state or administration, neither Aasen nor Knudsen feel any inclination to develop any new language, and the Norwegian dialects fare the same as the Swedish dialects, and are gradually replaced by Standard Swedish.
The Swedish system is very much centralised to Stockholm, with only small regional power, and the Norwegians adapt to this just like the rest of the country.
Since we do not have two administrations with different outlooks, but only one, the overall tensions would not be as outspoken as OTL, and things could be settled in Stockholm.
I wonder if the Norwegian church will joined to the Swedish church, or if they are to be separate. If so, this might be a national rallying point, so it might be better for the Swedes to have it united.
In OTL, Norway could develop institutions under the protection of the Union, and have a fully developed administration when independent in 1905. Here everything is part of the Swedish administration, and since the Swedish government, unlike OTL, has a strong Norwegian influence, why should there even be any Norwegian separatist feelings?
Perhaps the Swedish language keeps the three genders in this timeline. Many in Sweden still use them, and with added support from Norway it might be enough to avoid their abolition in 1900.
After democratisation in 1920, would the Norwegian people really care about independence? It is often claimed that nationalism is strong, and such is hard to comprehend from a Swedish perspective, since we are indoctrinated into non-nationalism. In this case, there has not been a Norwegian state for five hundred years, and the current state speaks the same language and has the same religion and is not geographically separated and there are no Norwegian institutions to rally around, and Norwegians are not discriminated or singled out in any way. Could they really care that much that they would feel it necessary to leave the Swedish realm? We have no lost war, such as broke Austria-Hungary, involved here.