(Forge 1.20.1)
I don't know if this is intended behavior or not, but it seems like furnace minecarts only power up (ie: start moving and using fuel) when they are chained to another minecart (ie: chain the minecarts, then power the furnace, and it starts moving. Put fuel in a solo furnace, nothing happens. Power the furnace, then chain the minecart, nothing happens).
If this is intended behavior, I believe it should be changed because:

• A player might want for a furnace minecart to go alone (to test a railroad, for example)
• A player might want to power up already chained minecarts (reuising a train that rain out of power without disassembling it)
• A player might want to create train in different ways (have the furnace minecart push the other carts without being linked, or use modded linking tools like Create's minecart couplings).

I think a furnace minecart should become powered when first fueled.
Hope that can help! have a nice day.

Understandable, this will be something I look into when working on the next minor update of the mod. May take some time though, because I want to port the mod to fabric first, and don't have much time to work on the mod rn.

At least the furnace minecart working separate from trains is definetly possible. I don't know about furnace minecarts pushing trains though, because that would require a rewrite of the whole chaining mechanic.