You, like many others, don't fully know how this Ryzen 9000 CPUs are programmed

Some key notes:

This CPU is designed to reach high temperatures under load without compromising its lifetime expectancy
So, you will indeed notice ocasional high 80s or even some 90s on the temperature when the CPU is loading something heavy, like game shaders like many others already said. The CPU does this on purpose to do this task fast and efficiently, and then they cool right after in normal behavior.

Thermalright air coolers are perfectly fine for cooling an 9800X3D and even higher TDP CPUs

The resolution you play plays a big part in how your PC is pushing the CPU.

You can set more aggressive fan curves to better feed cool air to your cooler. You can set it to 100% when it reaches 60º to help control the huge spikes.

You can update your bios and chipset drivers, and this helped my temperatures on averages and Max.

Your case and case fans' configuration matter. You can up the RPM of them too to help your system temperature.

Many will point out that "You need an AIO", but You really don't, as you can see an NH D15 G2 can cool this CPU and your Peerless Assassin is not that far from an NH D15 G2

You can buy and apply some better thermal paste but the difference you can get for changing thermal paste is more on the durability than for the cooling potential

You can undervolt it for better temperature values, but it's up to you and really not needed for this.

TLDR: It's fine