That's a difficult question to answer. I can try to shed some light on it for you from what I know from my own personal experience. The main one being: You might not get even 3600 Mhz ram to work in the X370 Taichi even with a 5000 series processor and faster ram. The X370 Taichi is going to run slower ram speed in general compared to say an X570 or even X470 system. Also latency matters a lot as well as capacity. Your current ram is clocked at latency of 15-15-15. If you upgraded to say the
F4-3600C16D-32GVKC kit then yes it would be 3600 Mhz but then you would increase the latency to 16-19-19 so your net gain of ram performance increase would be small or you may not see any increase in performance at all if you increased speed but with slow latency. You want to try to increase the speed but keep the same latency you have now or go faster (smaller number) in latency if possible. Also you should know about capacity. Higher capacity ram is going to reduce your possibility of running faster ram clocks with AMD. A 32GB (2x16) kit of ram may not run at 3600 mhz with any AMD 5000 series processor in any motherboard.
Here's a good option for you:
Are you a human?
32GB (2x16), Timings are faster than your ram at 14-14-14 (vs your 15-15-15), and it's only $199.99, which is right about where you wanted to pay. This is also right about the "sweet spot" in terms of compatibility that would most likely work in the X370 Taichi and a 5000 series chip. This would probably have a decent increase in performance at least +10% or a little more depending on the workload. For scenarios where you load the CPU to 100% on all cores and threads faster ram would be far more noticeable than light loads like gaming.
HP branded ram is kind of an "unknown" and if you would rather stick to name-brand ram here's a G.Skill kit of 3200, 32GB, 14-14-14 ram that's $209:
https://www.amazon.com/dp/B071VRMFDQ?linkCode=ogi&th=1&psc=1
3200 Mhz CL-14 ram is generally considered the "sweet spot" in performance for the AMD 5000 series chips in all platforms.