The proposed solution:
Add a new face for group tabs that can be configured via
'tab-line-tab-face-functions', similar to how
'tab-line-tab-face-special' works.

How to test:
1. emacs -Q
2. Apply the patch
3. Configure tab groups by project and group face:
(setq-default tab-line-tabs-buffer-group-function
          (lambda (b) (with-current-buffer b (vc-root-dir)))
          tab-line-tabs-function 'tab-line-tabs-buffer-groups
          tab-line-tab-face-functions '(tab-line-tab-face-group))
4. Enable tab-line-mode:
(global-tab-line-mode 1)
5. Open file from a project handled by some vc backend (e.g.: git)
6. The tab group will be displayed with a different face