Research from Earric Lee and/or Jari Laukkanen from this past decade will have clinical trials with controlled groups rather than just long-term population tracking. There are within-Finland studies comparing high-risk Finns who use the sauna 4 to 7 times a week against high-risk Finns who use it only once a week, showing a clear effect (https://pubmed.ncbi.nlm.nih.gov/25705824/). Here is a non-randomized experiment showing a dose-response (https://pubmed.ncbi.nlm.nih.gov/29048215/).
Those are just indications of information available. I would also argue that while of course randomized experiments are ideal, it is a mistake to dismiss all other forms of evidence so readily, especially with such preponderance of it.
Also, the fact that there are practically no sauna related studies outside of Nordic populations is suspicious too. I bet that with those hazards ratios a lot of people have tried to study the effects more, it’s suspicious there’s practically nothing out there.
There is a substantial body of existing research to peruse about the impact of regular sauna use on health outcomes, much of it from Finland given the prevalence of sauna usage there allowing for larger sample sizes. It's a body of evidence rather than one knock-out experimental design.