Browsers actually used to have hierarchical navigation support, with buttons and all, back in the age of dinosaurs - all one had to do is to set up some meta tags in HTML head section to tell which URL is "prev"/"next"/"up". Alas, this has proven too difficult for web developers, who eventually even forgot web was meant for documents at all, and at some point browsers just hid/removed those buttons since no one was using them anyway.
The "Back" remains, and as 'Arainach wrote, it's only one concept and it's not, and never has been "up one level in the hierarchy".
EDIT:
The accepted/expected standard way for "take me up one level in hierarchy" on the web is for the page itself to display the hierarchy e.g. as breadcrumbs. The standard way to go to top level of the page is through a clickable logo of the page/brand. Neither of those need, or should, involve changing behavior of browser controls.
In web browsers, there is only one concept.
There is no concept of "up one level in the heirarchy". If you want that make your own button in your website.
https://lifehacker.com/how-to-move-up-one-url-level-in-chrom... *shrug*
This statement makes no sense to non-tech people. Most people don't think of sites hierarchically, at least not from a url path perspective.
Going from an image to a root domain is not a hierarchy and as a pathological data hoarder who has downloaded a lot of images from a lot of sites I don't understand why I'd ever want that feature. It's wild that that's their first example use case on the article.
Similarly, going from page N of results to page 1 isn't "up a level in heirarchy".
*Edit - I left this in the wrong place, those extensions behave slightly differently.
Who expects this behavior? It doesn't make sense. You just want to go back where you were. Most file browsers I've used wanting to implement going up a level in hierarchy, have an arrow pointing up.
For example, the Bacula documentation is still online, as a prime example of this: https://www.bacula.org/9.6.x-manuals/en/main/Getting_Started...