connecting external hard drive to wifi network for time machine b/u

You don't have to turn off the Wi-Fi, but DO connect the Apple Airport extreme via Ethernet.

If you give it the same network-name and password, your devices use it in addition to your Eero Routers to "roam". They will select the fastest Wi-Fi pathway and switch off automatically.

This is similar to what the Eero Routers, do, except the Eero Routers hog a separate section of the 5GHz band to talk to each other (which means you can't use that band to talk to your devices).

Correct, it won’t be. Eero doesn’t support USB, only Ethernet. You have a USB drive. They won’t communicate, the adapter physically connects them but doesn’t allow communication.

You need a network attached storage enclosure. Personally, I have a QNAP NAS connected (via Ethernet) to my eero base station.

Did you try this (as in, not disabling your Airport Extreme's wifi)? I'd be overjoyed if it worked as Grant Bennet-Adler described, but this is the only place that I've seen it stated that if you leave the Airport's wifi on, it'll be used in addition to the Eero Routers to roam. The few other pieces of advice indicated that you should turn off wifi.

I'm going to be in the same situation soon, and am trying to plan ahead, so any feedback would be appreciated.

If you mean a typical external HDD that connects via some version of USB/TB, first you need a router that supports it, i.e. has a USB port. Do you have one?

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