This answers my question. But it’s not in terms of PHP code. I used the mysql command line client, once I figured out how to run it in my godaddy hosted WordPress environment:
The wp-config.php file has the DB_NAME, DB_USER, and DB_PASSWORD. And
the DB_HOST needs to be split at the “:” character to get the IP
address for the -h argument and the port number for the -P argument.
[I later learned that logging in to my godaddy account and accessing
its managed WordPress product gives a link to phpMyadmin, which
obviates the need to use the mysql command line client.]
Having gotten to the mysql command line prompt with the DB_NAME as the database in use, a simple show tables; does the trick:
MySQL [g5mb45616650937E]> show tables
+--------------------------------------------+
| Tables_in_g5mb45616650937 |
+--------------------------------------------+
| wp_6hanxjxbpv_actionscheduler_actions |
| wp_6hanxjxbpv_actionscheduler_claims |
| wp_6hanxjxbpv_actionscheduler_groups |
| wp_6hanxjxbpv_actionscheduler_logs |
| wp_6hanxjxbpv_booking |
| wp_6hanxjxbpv_booking_dates_props |
| wp_6hanxjxbpv_bookingdates |
| wp_6hanxjxbpv_bp_activity |
| wp_6hanxjxbpv_bp_activity_meta |
| wp_6hanxjxbpv_bp_friends |
| wp_6hanxjxbpv_bp_groups |
| wp_6hanxjxbpv_bp_groups_groupmeta |
| wp_6hanxjxbpv_bp_groups_members |
| wp_6hanxjxbpv_bp_invitations |
| wp_6hanxjxbpv_bp_messages_messages |
| wp_6hanxjxbpv_bp_messages_meta |
| wp_6hanxjxbpv_bp_messages_notices |
| wp_6hanxjxbpv_bp_messages_recipients |
| wp_6hanxjxbpv_bp_notifications |
| wp_6hanxjxbpv_bp_notifications_meta |
| wp_6hanxjxbpv_bp_optouts |
| wp_6hanxjxbpv_bp_user_blogs |
| wp_6hanxjxbpv_bp_user_blogs_blogmeta |
| wp_6hanxjxbpv_bp_xprofile_data |
| wp_6hanxjxbpv_bp_xprofile_fields |
| wp_6hanxjxbpv_bp_xprofile_groups |
| wp_6hanxjxbpv_bp_xprofile_meta |
| wp_6hanxjxbpv_commentmeta |
| wp_6hanxjxbpv_comments |
| wp_6hanxjxbpv_e_events |
| wp_6hanxjxbpv_links |
| wp_6hanxjxbpv_options |
| wp_6hanxjxbpv_postmeta |
| wp_6hanxjxbpv_posts |
| wp_6hanxjxbpv_prflxtrflds_field_values |
| wp_6hanxjxbpv_prflxtrflds_fields_id |
| wp_6hanxjxbpv_prflxtrflds_fields_meta |
| wp_6hanxjxbpv_prflxtrflds_roles_and_fields |
| wp_6hanxjxbpv_prflxtrflds_roles_id |
| wp_6hanxjxbpv_prflxtrflds_user_field_data |
| wp_6hanxjxbpv_prflxtrflds_user_roles |
| wp_6hanxjxbpv_signups |
| wp_6hanxjxbpv_tec_events |
| wp_6hanxjxbpv_tec_occurrences |
| wp_6hanxjxbpv_term_relationships |
| wp_6hanxjxbpv_term_taxonomy |
| wp_6hanxjxbpv_termmeta |
| wp_6hanxjxbpv_terms |
| wp_6hanxjxbpv_usermeta |
| wp_6hanxjxbpv_users |
| wp_6hanxjxbpv_wpaas_activity_log |
+--------------------------------------------+
As you can see, this output contains tables like wp_6hanxjxbpv_prflxtrflds_field_values (which I verified contained the phone numbers). I guess the prflxtrflds in the name is a vowel-stripped abbreviation for the name of the plugin Profile Extra Fields
This leaves me wondering why $wpdb->tables(‘all’) produces something different from mysql “SHOW TABLES”, and how can I use the methods of $wpdb to produce the same results as mysql “SHOW TABLES”. But those are different questions I will ask. Asked here