Alexander van den Berghe

It works fine for me in Emacs 29.3 and ob-async `20210428.20521`, tested with both async `20231105.1713` (version installed as dependency) and `20240323.1912` (installed explicitly for the purpose of testing this).

> Tabs are window configurations, if I understand correctly. I don't see why they must be dedicated to a particular frame. It should be possible to "move" a tab to...

You might want to look at [exwm-firefox-core](https://github.com/walseb/exwm-firefox-core/tree/master) and related packages for this kind of behaviour. Edit: More concretely, [exwm-firefox](https://codeberg.org/emacs-weirdware/exwm-firefox) seems to provide similar functionality, although keyboard-driven.

You could try setting the keybinding using something like `(exwm-input-set-key (kbd "") 'web-browser)` instead, this works for me irrelevant what kind of buffer is active.