Whilst the Eero may have Zigbee built into it (I am taking your word on this as I do not have an Eero), this is only the start of the problems.
Using any Zigbee devices with any 2.4GHz WiFi devices requires very careful channel allocation of both the WiFi & Zigbee APs/hubs.
Although Zigbee would see to use different channels to the WiFi ones within this band, the Zigbee ones actually sit within the same frequency spectrum as the 802.11 WiFi channels. Without analysing the WiFi spectrum and the Zigbee channels in use in your area, it will be hit & miss. I do not know of any Zigbee channel analysers.
