Nautilus is one neutered file manager. Let's have a comparison:
I will mention that I think the taller tab bar actually can help ground Firefox in the Gnome 'ecosystem' a bit better. Gnome uses fat title bars to stuff core app controls there. (Here's Gnome's web browser for comparison) Firefox has been using the narrow title bar design, which worked, but didn't quite "match" when put next to the other default Gnome apps like Files or Lollypop.
However, I will agree that this is and exceedingly bold move for everything out side of GTK. Title bars in Windows and QT are usually quite narrow. And either way, little else about Firefox's proton redesign currently matches the usual GTK elements anyways. So the "it matches Gnome" argument kinda falls flat quickly.
It has the folder, nautilus just also has a "shortcut" directly in your /home/methSC.
https://wiki.gnome.org/Apps/Files?action=AttachFile&do=get&target=general.png
The bar at the left is NOT directories but kind of bookmarks. The "home" there takes you directly to /usr/methSC.
And the bar at the top "lies"...that's what I meanted with some filemanager showing files on the root partition / and /home/methSC differently. Most peeople never have to leave their home folder...so always showing /home/methSC in front of every path is a waste. Nautilus shorts that to simply "home"
If you want to see how it really it follow /u/grg2014 advise...while being in your home folder ad using <alt><up> will NOT take you to root as you expect but rather to /home..and then you can see the folder in there with your account name.
So, no this is not OS specific usually ...pretty much all linux (and unix) systems do it like this. While it is theoretically possible to do it differently you will not find this by default on any of the major distros.