@Sqerly 

That's exactly right, a second EAP225 mounted on your workshop and you need will controller like the OC200.  The wrinkle is you have to move all your settings over to the controller unit (you will no longer have native access to the EAP225's standalone management interface).  It's a bit of a speed bump, but worth it once done.

The OC200 controller (or controller installed on a windows computer) can live somewhere in the house as long as it has access to the LAN that the EAP225's IP is on.  Then all you need to do is power the workshop EAP225 via the passive POE injector that comes in the box (keep this POE unit indoors BTW) and then some CAT5e or better out to the AP.  The Omada SDN solution should detect the new EAP225 and offer to Adopt it.  For the most part the buildings I mount the EAP225 on get enough service through the wall from that unit!  If you, you can extend your house LAN via the non-power port on the POE adapter to a switch or other AP.

Before you spend money on a controller and go through all this effort...you should try just mounting the EAP225 with a good line of sight to your workshop...you will be surprised how far that signal will go.

Now, if your workshop is metal clad...ie aluminum or steel siding/roofing, then you'll probably need one device on the outside to link and another device inside to broadcast to clients.

If your router isn't compatible with the controller (only ER605 and ER7206) and/or your switch isn't compatible with the Omada controller...you might be better off to you buy a point-point wifi bridge (or trench buried CAT5e).   Not sure if all your gear is TPLINK or not.

Anyways, share some more details about what you have gear wise and we can refine.