Both Intel and AMD typically release a set of chipsets for every generation of CPUs they put out. For the 13th generation of Intel processors, that's the 700 series of chipsets. For the 12th gen, that's the 600 series.
Both the 12th and 13th gen sockets share a socket though (LGA 1700), and Intel wants intercompatibility between all boards and CPUs that use this socket. The means allowing 12th gen CPUs to run on Z790 boards and 13th gen ones to run on Z690 boards. The former is easy to implement (just ship new Z790 board with a bios that supports the 12th gen chips). The latter is quite a bit harder, as a decent chunk of all boards produced were built before the 13th gen chips released, and are not compatible out of the box.
If you put a 13th gen part in a Z690 board that hasn't been updated at all, it won't work: the board does not recognize that CPU. Using a 13600k requires a bios update. ASUS/Gigabyte/MSI/etc can simply ship new Z690 boards with the newer BIOS out of the factory, but that still leaves quite a few existing boards (those sitting on shelves, in transit, etc) without the newer bios installed.
Some vendors might update the BIOS themselves before shipping, but it won't be universally done.
Point is you could end up with a board that uses an older version of the BIOS and isn't compatible with your CPU out of the box, and that's what PCPP is warning you about.
The solution is as simple as updating your bios, but given that this requires a CPU you might see how this is a catch22. Some boards include built-in hardware that allows for BIOS updates without a CPU, but it's far from the norm. Otherwise you'll need to get your hands on a 12th gen chip, which you'll either need to buy or that some manufacturers might lend you (I believe AMD did this a little while back iirc).