I recently updated to Brave Version 1.69.162 Chromium: 128.0.6613.120 (Official Build) (64-bit) and encountered the same problem. What fixed it for me was enabling a few options in brave://flags
Edit: Enabling these flags might cause a bug where Brave would create duplicate saved tab groups of opened groups everytime you exit Brave, which is annoying.
In that case please disable both ‘Tab Groups Save and Sync V2’ and ‘Tab group sync service migration’ flags.
Just keep the ‘Tab groups Save UI Update’ to ‘Enabled’. And manually delete the unwanted duplicates. That should work