You're right that present simple tense is often used for talking about habits or permanent situations. In this case, however, the statement is trying to emphasize that this is an ongoing occurrence (hence, the team is looking for new people at the very moment). "Our team always looks for new people" could mean that looking for new people is done constantly, but perhaps not at the very moment. An advanced nuance is also that the present progressive tense ("looking") seems more "active" in the action--which is being welcoming to new people. For example, this could make an applicant to the team more likely to apply.

It's a regular repeated occurrence. Like a habit.

You can use the present continuous: is always looking. Or the present simple: always looks