So I would grab Asus AI Suite through Armoury Crate and go into the Fan Xpert. Let it benchmark your fans and set the fans to have 0 sec fan spin up time and also go ahead and make it go parabolic to 100% at 50C-55C.
Before doing this ensure that:
Your heatsink is firmly on the CPU. It shouldn't move/jiggle at all.
You could have over-pasted the thermal paste. Remember you want a very thin layer. Just the size of half a Pea is honestly enough.
I recommend aftermarket thermal paste, and even an aftermarket cooler(literally anything except stock) because temps won't be good, especially on a CPU that's pulling up to 253 watts on turbo at stock.
"The Core i7 13700K with a TDP of up to 253W, consumes a lot of power, so it needs extremely good cooling. It supports DDR4 and DDR5 memory with a dual-channel interface. The Core i7-13700K also uses a PCI Express Gen 5 connection."
If all those bases are covered and that high of a temperature isn't sitting right with you, I'd undervolt the CPU, or, if you want to leave it be, purchase an aftermarket air cooler as long as you aren't considering overclocking, otherwise I'd do a water-cooling setup.
I don't know what the cooling setup is at stock for this processor, but honestly it should be water-cooled. But for a stock CPU I just feel that your reported temps under load are unacceptable in my opinion, if this is the idle temp, you definitely did something wrong in building the PC.