Clone Website on a New Installation to Update It

Hi there!

We need to recreate our site from scratch. When I mean from scratch I mean we want to keep the same content (pages, articles, URLs and tons of media) and move it to a new WordPress installation with a different theme.
A brief background to try to understand what the underlying problem is. The current site (the one to be copied and transferred) is HUGE. It has more than 1500 pages and 3000 articles. It is currently running on an old version of WordPress and an outdated theme. We are deliberately not updating WordPress, theme and PHP so as not to risk crashing and being left without a site (this has already happened in the past with another installation).
What we have done is to create (on the same hosting) a new, updated installation of WordPress (on another directory). This will be the new and definitive one. Then – when all is said and done – we should use the name of the first installation (but this will be another issue to deal with at the end). We decided to operate in this way because we want everything to be done as safely as possible.

Some details:

Objective: SITE 1 -> SITE 2

SITE 1:
Installation: domain.org/directory1
WordPress 5.2
PHP 7.1.33
Theme: Awaken

SITE 2:
Installation: domain.org/directory2
WordPress 5.7.1
PHP 7.1.33
Theme: Divi Builder

At the moment, we have already installed the new theme in directory2 and created the home page that will host all the pages and articles from the old site. We are not interested in keeping the plugins. Our aim is for the new installation to be as “clean” as possible, without the risk of dragging around old problems.
What do you think is the correct way to proceed? Again, the most important thing is that the links are not changed (so that the URLs will still work once the change has been made; I mean: domain.org/directory1/perma/link/article-written-in-the past = domain.org/directory2/perma/link/article-written-in-the past

Could the export/import tool do this job? How should I proceed to make sure that I don’t affect the performance of the new site? Is it possible to carry out a test with a few pages to see if this can be done?

Thank you all!