The problem
Firefox only auto-hides its toolbars in full-screen mode, which also hides the OS taskbar and the window controls. If you just want the maximum page area in a normal window, there is no supported way to get it. Extensions can't touch the browser UI, and the userChrome.css workaround needs an about:config pref and can break between releases.
Why it matters now
With vertical tabs, the only top toolbar left is the address bar. Hiding it frees a full row of vertical space on every page, which helps most on laptops and wide, short screens.
Prior art
Vivaldi's "UI Auto-hide" (Settings → Appearance) hides the interface, or any selection of toolbars, until the pointer reaches a window edge. It can also be limited to full screen.
Proposal
Add an "Auto-hide toolbars" option under Browser Layout:
Working prototype
I built this as a small userChrome.css, tested on Firefox 157 on Linux (Flatpak) with vertical tabs. It includes a short demo GIF, an installer, and a prototype extension with a settings page:
https://github.com/ericperuzzo/firefox-ui-autohide
It is only a stopgap. The extension needs an Experiment API, so it can't be published on addons.mozilla.org. A native option would make this available to everyone.