Tab Group Mover by Bima Janur

Tab Group Mover puts the current tab into a Firefox tab group without dragging. Open the toolbar popup, pick a group, done.
No mouse needed! All can be done using keyboard

What it does

Move the active tab into any existing group in this window or another window
Create a new group in this window (name is pre-filled from the site, e.g. github.com)
Leave the current group without closing the tab
Follow the tab after a move: it stays active and its window comes to the front
How to use

Switch to the tab you want to move
Open Tab Group Mover from the toolbar, or press the shortcut
Click New group, an existing group, or Leave current group
The group the tab is already in is shown as Here and is not selectable.

Keyboard

Windows / Linux: Ctrl+Shift+G
macOS: Alt+G
In the popup: arrow keys to highlight, Enter or Space to confirm
Change the shortcut anytime in about:addons → Manage Extension Shortcuts.

Requirements

Firefox 140 or later. Does not collect or transmit data.