I think what you’ll want to do – or something like what I’d do in your place – is create a simple WordPress plugin. (I’m bold-facing things that you can search up – lots of material on all of this will be right at your fingertips on the internet, often in detail in the WordPress Codex.)
On activation it would use wp_insert_post to create the pages you need. The pages would in turn all use the same page template – call it page-php.php or something. By some mixture of automation and hard coding, the page template would “include” whichever of your php sub-pages (or whatever you want to call them) at the appropriate points, along with whatever appropriate basic WP formatting and function tags. A typical method is to copy over the theme’s page.php, and use it is your template’s template.
For a general release plug-in, you might have to look into the more difficult tasks of programmatically producing page templates, or of utilizing custom post types. Either might actually be worth looking into, but I don’t think you really need to do so. On the WordPress All Pages screen, you’d just select and bulk edit your new pages to use the template file, which you’d add to your child theme directory.
For a general release plug-in you’d also probably want a way to add new pages and associated sub-pages to the group, but you could do that by hand if you weren’t able to arrive at a programmatic solution right off the bat.
As for whatever other necessary and unique JS and PHP files, all could be included as needed with the plugin.
I’ll just add that it’s possible to do this all with a child theme instead using very similar methods, and you will want to be working with a child theme anyway.
If and when you hit some roadblocks, you can come back here with the actual code you’re using and probably get prompt attention, and useful corrections and alternatives, very quickly.