I will see if I can find some good link. A little short I can say that Baptism first came to Sweden in 1848 and nine years later they had around 2000 members (in 45 Chruches), Anders wife Brita Stina one of them. After 1860 people where allowed to leave the Church of Sweden as long as they became members of an approved congregation. Until 1863 all Swedes had to take the Holy Communion or face a penalty. The monopoly of the Church of Sweden was one reason for people leaving Sweden for North America in the mid 19th Century. The most important reason for people moving away from Sweden from mid 1800's to early 1900's, was economical though because the increasing population in Sweden led to fewer people having the chance to get their own farm or even croft.
Well here is a link to some Englishman who writes about it. I have not read it all thru, but at least the part I saw was correct. I am not sure how safe this site is though but I guess it is ok. https://abritonthinicehockeyblog.wordpress.com/2019/04/22/new-protestant-revival-the-rise-of-the-swedish-free-church-in-the-19th-century/
Also here is a link to the Church of Sweden and their view of the History of Christianity in Sweden. Not much about the free Churches though: