I can’t get any of the tab keyboard shortcuts to work, even after chatting with email support for a while, nothing works.
Tried any combination of Tab + C or any other shortcuts, pressing exact same time, slightly one before the other, but the tab button always just sends the focus to the next text field like it would on a regular web form.
Tried on both my laptop built in keyboard and external USB keyboard.
None of the keyboard shortcuts works because the tab button just changes the focus to the next text field!
Your narration sounds like you’re expecting Tab-c to add a tag, but in fact that shortcut is actually Tab-t.
In your screencast at the end, holding down tab and then tapping “c” while tab is held down actually expanded the Comment textarea at the bottom of the task pane, as it is supposed to because Tab-c is for Comment.
So that manner of using tab seems to be working; try it with Tab-t.
Cmd+T in Chrome opens a new tab for me and Tab+T in Chrome/Asana opens the Asana task tag field. Maybe you have a non-standard Chrome shortcut set overriding the Aasna one?
Good sleuthing on the plugin idea! I think it’s pretty easy to check those; just go to: chrome://extensions/shortcuts and check all the shortcut key bindings there.