Can I provide a user’s user_ID to them and can it also be searchable in a member’s directory

This will give the user id of the currently logged in user:

$current_user_id = get_current_user_id();

User IDs are assigned sequentially (normally) when a user is created in WP admin (or by a process that creates the user ID programmatically).

But be aware that the user ID can be abused. For instance, one could query your site looking for a user ID of ‘1’ – which is usually the admin user. That could be information that could be used inappropriately.

And there are easy ways to enumerate all user IDs, by sequentially querying the site for user IDs. Another piece of information that could be used inappropriately (and has been to help attack sites).

So, whatever process you use to assign a user ID should take into account the possibility of abusing that information. Sequential user IDs can be a pathway to an attack on the site.

It might be better to use the user email address as an indentifier. With appropriate precautions to keeping that information secure.