Page hierarchy vs. redirects

I need to create a new version of an existing WordPress website using the Divi builder. The current site design is outdated and does not comply with many modern SEO and SERP standards.

A major issue is the site's flat structure. Currently, URLs follow the pattern http://www.domain/page.html, but they should reflect the site's navigation hierarchy, such as "http://www.domain/category/page.html." For instance, a page URL like "http://www.domain/wrench.html" should instead be "http://www.domain/tools/wrench.html."

With the recent changes in Google, AI, etc., how much will I gain in SEO if I restructure the new site to eliminate the flat hierarchy?

Permalinks don't matter as much for Silo/SEO,
It's a good way to make it easier for the bots/algo to know about the overall website silo,
But other permalinks would still do the work as long as the overall navigational/contextual internal links are in point,
The same goes for breadcrumbs, having them would help, but it's not a problem if they're missing, just one of the many on-page factors,
You can change the permalinks & use 301 along, nothing wrong with this, but it's simply not a must

Thanks!