There isn't any serious issue with that which I can foresee. But there would definitely be things in the root-level .htaccess now which aren't appropriate. e.g. The phpBB .htaccess provides a rule so that "any non-existent path" (such as /help/faq) will be re-written as a URL to be sent through APP.PHP (such as /app.php/help/faq). That's needed for phpBB, but will simply be "redirecting from one path which doesn't exist to an app.php path which doesn't exist either" when invoked at the root of the site.
Overall, I would say you're fine just putting the phpBB-based .htaccess in the phpBB folder only. It's not that "those things needed to inherit out to the root folder, too." But rather the other way, where we expected that things defined at the root folder (such as the HTTPS redirect) should have "inherited" or been processed first before the phpBB folder's .htaccess was processed (yet that didn't seem to be happening with the HTTPS redirect rule).
So you may indeed need to merge "things we have in the root" like the PHP handler and the HTTPS redirect into the phpBB folder's .htaccess. But not "the reverse direction", where you merge the phpBB-supplied rules and directives out to the root folder's .htaccess.
I don't know if the <IfModule php7_module> and <IfModule lsapi_module> blocks are still part of the .htaccess content you've retained. But the "php_flag display_errors Off" directive that was in there could possibly be changed to "On", at least temporarily, to see if in absence of an error_log this lets PHP emit the errors directly in the output (the HTML document) instead. Its usually better to have that turned off, since it can directly or indirectly disclose information about paths and configuration of the server in the details of the error.
But something you could do temporarily, as an attempt to make up for not having found an error_log for the phpBB folder yet. After purging the cache in phpBB ACP, see whether the "blank pages" change into something that reveals any more information.
It may not make a difference, because I think your old .htaccess files showed this parameter actually was "On" before, yet you didn't seem to be describing having seen any verbose PHP errors on the blank pages. But just something that comes to mind since the error_log hunt has not been fruitful yet.