Amine the exact anchor to the instructions regarding removing the public folder is https://docs.flarum.org/install/#customizing-paths
I assume those are the instruction you have followed. Do you still have a public
folder visible in the file explorer or have you successfully removed it from the filesystem?
What happens when you try accessing the website after having moved the files and deleted the folder?
The discussion you linked is still up to date. I don't think it's possible to be much more detailed than the discussion explains. But if you have error messages we can help you with the specific messages.
I don't know whether Softaculous allows customizing the website root? There's often a setting in managed hostings where you can put the path to your website on disk. Because that would have been the easiest method. Our default installation strategy is to keep the public
folder on disk and just tell the webserver that's the new root folder.
I've seen multiple people talk about Softaculous recently so someone who has done it might be able to provide better information. I haven't tried Softaculous myself but I'm surprised they don't configure the webroot correctly as part of the automated Flarum installation.