there are pathways to produce synthetic oil from coal or using carbon capture if you have cheap energy. I hope they will catch up if fossil oil prices skyrocket.

This is the secret flipside of solar power's duck curve: it makes a lot of stupidly energy intensive paths towards non-fossil oil production a lot less stupid if you just have the energy to burn. Think about how in the 2000s we had a weird obsession with ethanol and other biofuels, only to learn that they were merely 40-50% efficient. If your energy mix is predominantly fossil fuels, you're better off just not burning the oil. But if you have solar, suddenly it becomes a good option for energy storage, especially in industries that need the weight properties of chemical fuels (i.e. aircraft, where you HAVE to be able to burn and exhaust your fuel or the plane will be too heavy to land).

Pretty much all chemical changes can be made with reasonable amounts of energy. That includes making "bioplastics" as well as the typical plastics we use today like polyethylene, polystyrol and so on, from biomaterials. What doesn't work in a way that's remotely economical is transmuting elements. It is, for example, possible to make gold today, the old dream of alchemists. But it's several orders of magnitude too expensive.

Common plastics are made from highly abundant elements, so running out of oil as a chemical feedstock is a quite surmountable problem given cheap enough energy.