Thank you. In my config, I've also implemented "(setq tab-bar-inhibit-inactive-group-tab-hints t)" which suppresses tab hints on group tabs when inactive groups are being displayed as they are generally superfluous in that case. We could make suppressing tab hints on group tabs when inactive groups are being displayed as the only behavior which is also fine by me.
(defun my/tab-bar-tab-group-format-function (tab i &optional current-p)
(let ((tab-bar-tab-hints
(if (and tab-bar-show-inactive-group-tabs
tab-bar-inhibit-inactive-group-tab-hints)
nil
tab-bar-tab-hints)))
(concat
(propertize
my:tab-bar-tab-group-name-prefix
'face (if current-p 'tab-bar-tab-group-current 'tab-bar-tab-group-inactive))
(tab-bar-tab-group-format-default tab i current-p))))