I see that you have 281 552 posts in total. First of all, congratulations for establishing such a successful community! It is nice to see someone using FreeFlarum to achieve a milestone like that.
However, I have to mention, the activity of your forum is way past the limits described in the Fair Use Policy. While these limits are not enforced, it also means that FreeFlarum does not provide any warranty and uptime or functionality guarantees, etc… It is a free service after all, and I hope you understand that
Now, for the actual problem: yes, the request is timing out. FreeFlarum limits the maximum PHP execution time to 30 seconds, which matches your observation.
As for what can be done: I understand that you (and your users) have the right to download their data. This is okay, which is why I am offering to temporarily (1 week?) increase the timeout limit for your forum, so you may give your users the opportunity to download their data - if you confirm?
However, please note that for a long term solution, you should really move your community to a different hosting (migrate away from FreeFlarum). You can download your full forum database dump and assets at anytime here and import it to a different host. If you are looking for something similar to FreeFlarum, I recommend this managed hosting service: https://flarum.org/hosting
