Relays can be used for anything, and a car contains a fair number.
You can make a pulse jet engine from a muffler parts, but a solarpunk society would probably not do that. :)
Copper brake pipe and cooling radiators can be used as heat exchangers for other stuff.
Air conditioner parts can be reverse-used for Stirling engines or to pump heat in other contexts.
I'm not a chemist either, but I do know a bit of chemistry.
Typically, you need a solution of NaOH (sodium hydroxide) to directly reduce iron oxide in an electrolysis cell. If your iron oxide contains impurities, those may react with NaOH and ruin the fun. Also, if you have exposure to CO2, your NaOH will gradually degrade, producing NaHCO3 and losing potency.
My impression: wet electrolysis is great for making high purity iron, but it would be hard to make it work for energy storage.