The Code says the foundation need to be “adequate” for all loads.
Most people think of vertical loads, but there are horizontal loads, freeze/thaw loads, etc.
I too live where the ground is mush. Usually we install piling, caissons, etc. However, in certain situations we install a “floating slab”.
This system is a structural slab (with reinforcing steel) with edges that turn down about 12” at the edges. (We don’t have a frost freeze/thaw issue here. If you do, you may want to extend it somewhat.) We install about double the amount of reinforcing steel than we use in stem walls.
We use this system for small, simple, fairly symmetrical buildings...which sounds like your project.
You’ll have one additional issue of where it connects into your existing house. Because your house is on piling, it will not move (settle) over time. Therefore, I’d recommend the structure be a few feet from your existing house where you can plan for a few inches of settlement. The connection space between the two structures can fasten (rest on) on both structures and flex when the conservatory settles slightly.
In fact, installing augured piling, hammered piling, etc. next to your home may cause significant damage (cracking plaster, cracking windows, etc.)
Any plumbing or electrical supply lines should have blockouts through the slab so it’s flexible.
Because of all that glass in your conservatory and you don’t want any differential settlement in the walls, I’d recommend you design the perimeter foundation as a concrete beam. You’ll probably need an architect or structural engineer (not a civil engineer) to help you.