3200MHz CL16 is exactly the line where you should be fine. I assume you have 2x8GB, right? Which game did you notice an improvment when pushing to 3600MHz? You may also gain/lose a few percent if you put them in the correct/wrong slots - look in your mainboard manual if you are unsure.
Yeah I agree with the minimum fps and maximum frametimes. 33.3% higher (I assume average) fps because of 12.5% faster RAM sounds implausible.
Go for DDR5 since you do not attempt a super budget build. DDR4 is outdated and DDR5 not so new anymore that they are super expensive.
If possible go for 2x8 over 1x16, but they are most of the time sold as a kit anyways. The two most important numbers are the frequency and the CAS latency (CL). Do not forget about the latter!
I think the LGA1700 socket only supports 12th-14th generation (which is why I personally went with the R5 7600). You should keep in mind that your upgrade options would be limited and the re-sale value of the 13500 will be low (people may want to upgrade from their i5 12500 to an i7 14700, but not to your 13500). For this reason you may want to consider a better CPU, but then again the 14th generation is just a refresh and not that much better.
Ah ok, so definitely enough and all slots filled :)
Any benchmark I have seen for the i9-13900k showed good improvements up to 3200MHz (CL16) but only little beyond that. The fastest DDR5 RAM in games is usually <10% faster than mediocre DDR4 RAM.
Regarding Tarkov I saw in detail tests with other CPUs where RAM speed did not really matter - well beyond 3200, there is a Reddit post from someone increasing it from 2133 which helped him a lot (in line with what I saw and wrote before).