I wonder if there’d be new fossil fuel deposits by then.

Probably not. Coal is basically trees that didn't rot, and the reason they didn't rot is that there were no microorganisms that could digest wood at the time. Between the evolution of wood and the evolution of organisms that could digest it, dead trees would just pile up on top of each other and sink into the ground under the weight of new layers of dead trees above them. Now that there are microorganisms that digest wood and dead trees rot away, new coal is not forming.

Oil does continue to form in some ocean areas where there is a layer of water without any oxygen on the ocean floor. Since these areas support no life, any organic remains that descend to the bottom (mostly plankton) remain unconsumed and eventually get buried and turn into oil. But it is a slow process. Estimating oil reserves is notoriously difficult, but it seems there's about as much left in the ground as we've burned in the last fifty years. So in other words, four billion years of oil formation gets you about a century or two of industry. Since the Sun is about halfway through its lifespan, that means the Earth can potentially create enough juice for one more industrial civilization like ours. That's assuming that those oil reserves are allowed to build up and don't just get used up piecemeal by smaller civilizations arising in the interim. And also assuming that that final civilization is even able to make use of that oil, which is much harder to handle than coal (extraction, refining, transportation, etc.), without using coal as a stepping stone. And also assuming that no anaerobic microorganisms evolve that can survive on the ocean floor without oxygen and consume those organic remains, which could put a stop to oil formation just like wood-eating microorganisms put a stop to coal formation. Yeah, that seems like a lot of ifs to me...