What PC upgrades would give me the biggest gaming boost for around $800?

The best choice depends on the games you play. For demanding 1440p games, spend most of the budget on the graphics card. For competitive games targeting very high frame rates, a 5700X3D-type CPU upgrade can be worthwhile while keeping your motherboard, RAM, and storage. Check your power supply, case clearance, and cooling before choosing a new GPU.

Since you play at 1440p, the graphics card is probably the biggest limitation. A stronger GPU should give you a much larger improvement than replacing your already adequate 32GB of RAM. You could look at a current midrange card and put whatever remains toward a CPU upgrade later. A Ryzen 7 5700X3D or 5500X3D-class chip would also be a great drop-in upgrade for the AM4 platform, especially for esports and CPU-heavy games, but fitting both a major CPU and GPU upgrade into $800 may be difficult.

Storage is the easiest inexpensive quality-of-life upgrade. Replacing the ancient hard drives with a larger SATA SSD or NVMe drive would make game installs and general use much nicer, but it will not improve gaming frame rates. If the old drives are showing errors or making unusual noises, back them up and replace them soon.

Your memory is fine if it is running at DDR4-3200, so there is no need to replace it just because a monitoring tool shows around 1600 MHz. DDR memory reports its real clock speed, and DDR4-3200 commonly appears as roughly 1600 MHz. I would prioritize the GPU rather than buying another 32GB kit.