Some eero hardware does support power over ethernet (PoE+). To provide power to your eeros, you should use the supplied power adapter.
If you have an eero PoE+ adapter, an eero Pro (not the Pro 6) can be powered over Ethernet using the necessary PoE+ adapter, injector, or a 3rd party PoE+ switch. You can review Suggested injectors and PoE+ switches.
eero PoE 6 can be powered via PoE (802.3af) with a Cat5e cable or higher and a supported PoE switch/injector. eero 15w power adapters are compatible with eero PoE 6 and may be purchased separately. Please visit here to purchase the correct adapter for your eero.