I had this problem without an easy solution, so I did one wich worked perfectly.
To add the logged in user profile link to a Elementor Widget, do this:
Add a custom shortcode to your theme functions.php
// Custom Buddypress User Profile Link
function custom_bp_user_link( $atts ){
return bp_loggedin_user_domain();;
}
add_shortcode( 'bp_user_link', 'custom_bp_user_link' );
After this, go to Elementor and in the link option of your widget select “Custom URL”, then select “Shortcode” and add
[bp_user_link]