Hi Ethan,
I am sorry I missed your post earlier.
Are you on multisite? If yes, you can add the following line to bp-custom.php to enable the default email

add_filter( 'wpmu_welcome_notification', '__return_true', 111 );
add_filter( 'wpmu_welcome_user_notification', '__return_true', 111 );

If you are not on multisite, BuddyPress does not send any welcome email. I had written a post long ao that allows doing it. You may find it useful
https://buddydev.com/buddypress/send-welcome-email-to-users-when-they-activate-their-account-on-wordpress-buddypress-based-social-network/

Hope that helps.

Regards
Brajesh