TL;DR: have 1 such jacket experience - do not recommend
My workshop is also unheated and I own one of those jackets (some far eastern noname) which works from any power bank with a USB socket.
Could not get on with the jacket and prefer to put on more layers than use such jacket.
- Small/light battery does not last. Large battery makes it too heavy and uncomfortable
- When I move about the workshop in the heated jacket it gets uncomfortably warm in just few minutes so I have to keep turning it off and on (mostly off)
- my jacket has reflective (non breathable) inner layer which causes excessive perspiration
I could see this jacked being useful if I sat in one spot all day (not moving much), but if that was the case I probably won't be sitting in the workshop.
If I was to consider such jacked again it would have to have two improvements
1. no plastic (non breathable) layers
2. some way of spreading the weight of the battery evenly and without asymmetric bulge anywhere