My garage / workshop sounds very similar. With draughts where it’s impossible to fill because of how the ( old) up n over door has to work.
Fitted a brush type draught excluder to the lower edge of the door though.
Carpeted the whole thing with old carpet, when we replaced some in the house and use an old hearth rug for where I mostly stand.
I bought a pair of real cheap heavily padded skate shoes, deliberately a size too big. I wear those with wool winter walking socks and have cut a layer of bubble wrap and put it under the insole. I have another similar pair of socks which I leave in the house, when I come back in to get another brew on, I change the socks, for the warm ones.
I notice a huge difference if I just gout out here for an hour or so in ordinary socks and trainers.
Depending how cold a day it is, I just layer up, thermal base inc long johns, wool jumper, jeans , beanie. A boiler suit and body warmer too, on real nippy ones.
My feet probably stay warmer at 2degs in the garage than they do on winter rides.