I almost don't dare to ask - but what is a wireless bridge vs a booster.A wifi booster is not going to work. Get a wireless bridge and put that in the shed. You will then have internet out in the shed.
I would recommend a camera like Reolink or Foscam, or Swann. They have been around a long time and work great.
This is a Swann camera which works with my Reolink application. The chickies love Reenie’s stall as she leave all sorts of goodies to eat
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This is a Reolink (this one is a Pan Tilt Zoom, 3 times zoom).
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PM me if you want any technical assistance.