How can I include a Users picker in a custom field type?
I don't know your requirements, but you could build a "Users Picker" with the Dynamic Fields plugin. You would basically need to do the same in its settings to build your select options as you'd do in a custom plugin.

You get your users with craft.users and then build an array with "label" and "value" keys using the merge filter.

Pass that array into the Dynamic Fields' settings or build the select options with the forms.selectField macro in your own plugin.

{% set users = craft.users.group('clients') %}

{% set userOptions = [] %}
{% for user in users %}
    {% set userOptions = userOptions|merge([{ label: user.friendlyName, value: user.id }]) %}
{% endfor %}

{{ forms.selectField({
    label: 'User'|t,
    id: id,
    name: name,
    options: userOptions,
    value: value ? value
}) }}