The fossil fuels (oil, gas, coal) are non-renewable (with a replacement time of hundreds of millions of years) and as such are indisputably finite. Their extraction absolutely will cease some day. But long before extraction ceases (“oil runs out”), it becomes difficult and expensive, and the oil supply will begin to shrink, and that’s the problem under discussion.
It is indeed not the first time that production difficulties have arisen. When some European countries had stripped their forests of wood they were forced to dig for coal, at much higher cost in human labor, lives, and pollution. When whale populations declined, whale oil became so expensive that it eventually made sense to (dangerously) refine tar into kerosene. In our turn, “switching” (resources) will take decades at least, due to the time-lags and costs of infrastructure replacement.
“Known reserves are higher than ever”? Only if you believe the OPEC countries, which claim 2/3 of the global total, and have been manifestly dishonest about their reserves since 1985. That was when they decided that each OPEC country could sell an amount of oil proportional to the country's claimed reserves, so all the countries simultaneously increased their claimed reserves by 50 - 100%, and they have not come down since. How much they do have left is a most key question, but they have much economic incentive to go on exaggerating and prevent inspections. A couple of their retired officials have become whistle-blowers, e.g. Samsam Bakhtiari and Sadad al-Husseini; they are of course vigorously pooh-poohed by their countries. An expert assessment of the state of Saudi oil fields leads to the conclusion that there are less reserves than claimed (see Simmons' book).