You wouldn't recover the propane at the exhaust of the car. Instead, you'd have a fixed hydro/solar/wind renewable energy installation, spending ~25 kWh on an atmospheric capture program, or less if you can get it from more concentrated flue gasses coming off an industrial furnace/ammonia plant/cement plant, and then ~200 kWh to convert that CO2 by this process into 100 kWh worth of LPG.
It's not viable (in terms of energy availability, packaging, or economies of scale) to run that sort of cryogenic high-pressure CO2 purification and storage system on the exhaust pipe of a vehicle. I could maybe imagine a solar installation with this attached being viable at, say, a remote farm with LPG-powered agricultural vehicles, or if I stretch my imagination to scifi timescales (and think about the number of remarkable compressors installed at scale in HVAC systems) to suburban homes with rooftop solar.
I don't think it's ever going to be viable at the suburban level. However, for off-grid use I can definitely see it making sense. Large scale batteries for photovoltaic use make off-grid solar quite expensive on kWh basis. This is considerably less efficient (although I think you could up the efficiency with a turbine generator) but costs scale on throughput, not on capacity.
It's not viable (in terms of energy availability, packaging, or economies of scale) to run that sort of cryogenic high-pressure CO2 purification and storage system on the exhaust pipe of a vehicle. I could maybe imagine a solar installation with this attached being viable at, say, a remote farm with LPG-powered agricultural vehicles, or if I stretch my imagination to scifi timescales (and think about the number of remarkable compressors installed at scale in HVAC systems) to suburban homes with rooftop solar.