The forum should be used to announce Tournaments, review applications, and resolve any issues. The actual statistics should be kept on the website, but separately from the forum. There, participants will naturally fill out reports in a standardized format, attach save files, screenshots, etc., and the ranking will also be there. This will make things easier for those who manage the reports and those who read them. In addition, there is an opportunity to develop and improve the system. An archive of Tournaments by date, current Tournaments, and just games. All names and in-game titles should be selected from a list. A simple and clear interface. It should be convenient.

I don't see any advantage in such a separation. It's much more convenient to write a report with the results in the Tournament thread as usual, and the results are automatically transferred to the statistics and ranking thread - without the reports, only the result itself.
And how the results are sorted in the statistics is a different question.
It is clear that it would be desirable to have the option to view statistics separately for each Tournament. It would also be useful to have links from the statistics thread to the corresponding posts with the reports.

It seems that the most convenient thing would be to add two more buttons to each of these three places - "Write Report" and "Confirm Report".

But it needs to be so that the confirmation with the report is automatically redirected to the correct thread. So that it doesn't happen that you open the form in one thread, and the confirmation and report remain there.
It would be better if the confirmation button appeared only for users with unconfirmed reports. And a message about the presence of unconfirmed reports upon login would also be helpful.