The metabolism is to simply wait for resources to react naturally. PNA in sufficient concentrations and conditions will continue to polymerize and grow just by random chance. It's not any different from what happens inside a simple cell, really: ATP and other resources are for the most part just present inside the cell. It's just that for life to come about those conditions or something like them have to exist naturally.

As the RNA/pre-RNA chain grows, there will be natural selection for any sequences that catalyze polymerization. This will eventually either lead to self-catalyzing replication or a mutual replication. AFAIK the second one is considered more likely because although RNA can self-catalyze it's not very good at it (of course, it doesn't really need to be). Mutual replication would require a primitive polymerase being spontaneously generated, which would allow an RNA-like molecule to -self-replicate. Eventually an chain would be created that could replicate via copies of itself, and that molecule would be able to spread beyond the original catalyzing molecule and outcompete anything else (since it would be able to replicate with any copies it made, it would grow exponentially rather than linearly).