Malaka We don't have any formal approval process or checking, but many of Flarum's staff members are behind the extension group Friends of Flarum, and they use plenty of extensions made by our many talented community developers. So even if our staff doesn't catch a problem with extensions posted here, our community usually does, and you can see a recent example of how one extension was fixed with the help of the community.
We have yet to find a malicious extension or one that was unintentionally providing a security hole through the extension itself. You don't need to be worried about the caliber of extensions here, any listed in the Extensions tag we keep an eye on and add an INCOMPATIBLE tag if they are no longer working in the latest Flarum version, and we ensure that the extensions are ready for use and not half-completed/WIP.
If you do come across an extension that you encounter a bug or security problem with, please do report it to the developer in their extension discussion or Github issue tracker. You can also use composer remove vendor/extensionname to remove and disable the extension if it is misbehaving, and most of the extensions posted here will provide that command as well.
I hope that answers your question and assuages any concerns you have.
