Since I lived here n Budapest twice and learned the language, I’m somewhat familiar with this topic. Of the original Magyar tribes which migrated westward and settled on the Hungarian plains in 1100, not that much remains of their genetic stock even though the language and culture survived. They became pretty intermixed with the Slavs and Germans in the area. A couple times the population was devastated by plagues and they invited in Swabians (southwestern Germans) as well as some neighboring Slavic people (Czechs, Slovaks, Croats, etc)to help repopulate.
About the language.....if I hear Finnish in the next room behind a closed door for example so it’s a little muffled,then it does sound like Hungarian a bit. Some of the sounds are similar. I can’t understand a damn word of Finnish though even though the languages are related. Its not like say English/Dutch/German which share many words and many more which are extremely close ifnot exactly the same.
I've never heard anyone speak Finnish, which is why I'm asking you, since you have heard it spoken.
You are right, and here is more info “The relationship between the Finnish and the Hungarian languages” https://histdoc.net/sounds/hungary.html