If you want a soft, insulated floor, there's nothing (apart from the inevitable soiling) saying you couldn't just leave the carpet, cutting holes in it to allow you to have machine/bench feet directly in contact with the floor as required.
This is unconventional, but would be both the cheapest option by far and reduce the amount of effort to do the workshop up.
I would consider NoMorePly boards, intended as an underlay for tiles and for stabilising old wooden floors, but has lots of workshop friendly properties:
- impervious to moisture,
- fireproof,
- insulating,
- impact resistant,
- dimensionally stable.
You then have a choice to either use a floor-paint (I like 2-pack polyaspartic [a type of PU paint] for it's self healing properties, but epoxy is a bit more hardwearing to begin with and lots of 1-pack paints are very good just very solvent-y), or buy cheap foam tiles which you can cut to neatly fit anywhere you don't have machines/benches on the floor, and bond down with contact adhesive if you desire.
The foam tiles add cushioning and insulation, whilst wearing unreasonably well considering how inexpensive they are; I guess you could lay them direct onto a wooden floor, but the likelihood of it remaining good long term is limited.
In both cases I am assuming being a tiny wooden building, you'd do any heating / soldering / brazing with open flame, outside the workshop, making a flammable floor covering (carpet or foam tiles) acceptable.
If you do intend to do this inside, nomoreply or steel chequer plate, with paint are better options.