Not sure what posts you've already read, but the main reason you might choose to do "more than just dropping a favicon in the root of the site" is when you want to provide platform-appropriate representations which allow assets that are larger than what a favicon can provide. Starting with just the favicon.ico is fine, and you can always do more later when you want to.
By "more" I mean instead of users of these other platform representations seeing a stretched 32x32 or 48x48 favicon.ico image, they see up to a full 256x256 or 512x512 image containing either the same or a completely different image for representing your site in these higher-resolution scenarios. Plus for some platforms an icon background or border color choice that is unique to your site.
For example,
https://realfavicongenerator.net/ will help you generate not just an appropriate favicon.ico, but also an image appropriate for an iOS home screen icon the user may create for your site, an Android home screen icon the user may create for your site, an image that Windows 10 and Windows 8 would use if users pin your web site, etc. Hit the "Demo with random image" button on the site to be shown an example of the different platforms it supports and the options for each one.
Yes, this involves a bunch of meta tags that need to be added to the HTML that your phpBB site generates, which is something you could maintain along with other style customizations you're already maintaining, or you could find a phpBB extension which lets you add
<head>
data to your pages without having to modify the style. The
https://realfavicongenerator.net/ site provides you with exactly what all the needed HTML directives are, along with providing the actual assets themselves.
For example,
this post shows what was added to the overall_header.html to make use of all the assets generated by the site.