Looks like it'll work.
I'd be *slightly* concerned that if you put the shop-side unit facing the house, if your phone is 'behind' the shop-side unit, how far away can it get ?
Honestly, no idea, but it'll probably be fine.
https://www.engeniustech.com/resources/ENH500%20User%20Manual%20v.1.0.pdf
looks like you put both of them in "access-point" mode and maybe put the shop-side on far side of the shop, so that your phone and stuff are between both units.
I'm a fan of the "cable and OTS wifi router" approach - if the distance isn't too far (must be less than 100m/300ft)
...only because once you have a cable, you can put anything you want at the far end (and replace stuff more easily if something breaks)
They sell 300ft cables but the easier answer is to make friends with your IT person/electrician at work, who probably has a spool of the stuff lying around or a long piece that he/she is trying to get rid of.... Run the cable out to your shop as best you can.
This is the cheapest way, there are better ways (conduit, patch panels at the house and in the shop, fiber runs with converters on each side (and spare fibers...), but I'm not sure how much time/effort you want to put into installation.
bottom line - what you linked to should work, but I've never tried this before - maybe someone else on here can point you better.
-John