Can I use Jax's legend ability to reattach an equipment to the same unit it's already attached to? For example, reattaching Brutalizer to regain the +2 might bonus, or reattaching equipment to Aphelios to trigger his effects?

No. Under Rule 434.1 (added in the Unleashed update), attaching a card to its current top-most card (the unit it's already attached to) has no effect. You can no longer reattach Brutalizer to the same unit to regain the +2 might bonus, and you can no longer reattach equipment already on Aphelios to trigger his effects. The equipment must be attached to a different unit for the attach action to have any effect.