How does this £1,500–£1,600 first PC build look for high-FPS gaming?

The Peerless Assassin is a strong choice for the processor, and an 850W RM850e gives you plenty of power headroom for this graphics card. I would be more concerned about buying a reliable SSD and leaving room in the budget for a larger drive, since 1TB can fill quickly once Windows, applications, and several large games are installed. For Windows, use a legitimate retail or OEM license from a reputable seller rather than an unusually cheap key with an uncertain source.

The biggest issue is the balance between the CPU, motherboard, and graphics card. A 9800X3D paired with an X870E board is extremely high-end, while an 8GB RTX 5060 Ti will be the limiting part in many modern games, especially at 1440p. For competitive shooters it can still deliver high frame rates, but the system would generally be more balanced with a less expensive AM5 motherboard and CPU, then putting the savings toward a 12GB or 16GB graphics card. A B850 or B650E board should be more than enough unless you specifically need the extra connectivity of X870E. Also double-check the memory price, because £329 for 32GB of DDR5-6000 is unusually high; CL30 memory would be preferable if it is similarly priced.

For your target games, the 9800X3D can make sense if you are seriously chasing very high refresh-rate performance, but it is not essential for every game on this list. The GPU will matter much more at 1440p and in visually demanding games. I would compare complete system prices before buying and avoid paying a premium for the motherboard or decorative fans if that money could move you to a stronger GPU. Make sure the case actually has good ventilation rather than simply counting the number of included fans, and check that the extra fans use a sensible intake and exhaust layout.

You generally do not need an anti-static wrist strap at home. Build on a hard surface rather than carpet, keep the PSU switched off but plugged into a grounded outlet, and touch the bare metal part of the PSU or case before handling components. Repeat that occasionally and avoid building while wearing static-prone clothing. A strap is inexpensive and can provide peace of mind, but careful handling is usually enough.

Wallpaper Engine normally has a small impact, but you can reduce it by setting wallpapers to pause or completely stop when a game or other fullscreen application is running. Use lower-resolution wallpapers, avoid demanding 3D or audio-reactive scenes, cap their frame rate, and disable hardware acceleration if a particular wallpaper causes stuttering. For competitive games, having it pause automatically is the safest option.