Do not sync menus in WP admin - WPML - Menu translations
Refresh BuddyPress Navigation in each language
After setting up each menu, make sure you click on BuddyPress refresh navigation button at WP Admin - Vibebp - settings - buddypress for each language.
Note if you add new plugins to the PWA / Members area, then you'll need to follow this step again.
Use BuddyPress Single page
Enable BuddyPress single page and make sure the translated version of each page is available.