unfortunately Pro plan doesn’t include data explorer or automation plugin because i think those could be used for a solution here.
normally i would just suggest extracting the custom user field data via data explorer query.
however, you should be able to filter on the users page at /u, once the new custom field has some values from users.
have you read this topic yet? Creating and configuring custom user fields
to give an example using the automation plugin - i would configure an automation to add the users to a group based on the user field then you would always have them grouped accordingly. for example you might have 3 groups based on a custom field with 3 options, then you could use a data explorer query (automated or manual) to extract the email addresses of those group members into separate lists (or use the automation to send DM to group members).
data explorer query to get email addresses of group members
-- [params]
-- string :group_name
SELECT
u.username,
ue.email
FROM users u
JOIN group_users gu ON gu.user_id = u.id
JOIN groups g ON g.id = gu.group_id
JOIN user_emails ue ON ue.user_id = u.id
WHERE g.name = :group_name
AND ue.primary = true
ORDER BY u.username