A wooden structure does not necessarily mean a shed, depends how it has been installed and adapted.
Jason, according to your description you have a wooden building that is soundly supported on a concrete base using close spaced heavy duty timbers, thick ply flooring and insulation. That structure been designed and built from the ground up to be a workshop and mine is similar.
You are in shed territory when the structure sits on the bare ground or slabs or the ridiculously expensive plastic honeycomb they try to flog you. It is a shed when the structure is spindly 25mm timber, with thin untreated cladding (usually with plenty of knot holes), 12mm flooring and without any damp protection or insulation.
The point I was making is that there is a significant cost adjustment between what is acceptable for a shed (for the garden tools etc.) and what is needed for a reasonably dry and stable workshop environment, which I would expect yours to be, because that is how you planned it.
Thinking about the OP, I am sure that a structure can be acquired within budget but will that budget be sufficient to cover all of the extra requirements to make that structure a suitable workshop.
Sadly for the OP it is not just a case of sourcing the lowest cost unit, plonking it on the ground, moving his lathe or whatever in and jobs a good’un…. If only life was that simple. In this scenario, joy will turn to angst as his shiny new tools start to take on the rust and patina of well aged garden implements in a short space of time.