Generalizing like that almost never works. Also if anything it's the opposite. I don't really see a 2200G/3200G winning against even an i3-9100, especially in games. Or even a 2400G/3400G and those are significantly more expensive. The 1200 is so outdated it's not even fair anymore and the 2300X is OEM only. If you don't need the GPU of the G a 9100F costs about the same as a 1200 and it's not even close. So if you want a fast quad core there's not a whole lot on the AMD side. On the other hand if you just want more threads and the per core/thread speed doesn't really matter it's hard to argue with the 1600 12nm refresh. 85$ for 6 cores/12 threads. Same at the high end. Yeah sure, a 9900K is faster per core/thread, but either you're buying 8 cores/16 threads for no reason or a 12 core/24 thread 3900X is going to run circles around it. Anything in between, especially for games, it's not so clear-cut. There are enough games where more than 4 cores do help (not TF2) but more than 8 threads not so much. It's nice that the 3600(X)/3700X/3800X come with SMT, but it barely makes a difference so 9600(K/F/KF)/9700(K/F/KF) are actually worth considering.
Going blindly by brand and the choosing whatever's most popular is a really bad idea. Popularity is rarely an indicator of quality nor is there any guarantee that what works best for someone else works best for you. If you're doing the same thing sure, but TF2 has always been a special case.
Anyway I'd say either drop down to 4 cores, which'll do fine for TF2, or go for higher clockrates and faster RAM.
3600X is kind of meh, 3600 should get you almost the same performance, especially if you overclock it, but the upside of TF2 being shit is that even those 0.2 GHz could get you another +5% fps. RAM is more important. Getting 3600 MHz RAM is going to do more than getting a 3600X instead of a 3600. At the very least don't go below 3200.
Not sure if a 9400F would be faster (it's definitely cheaper though) but a 9600(KF) definitely would be.
For quadcores the previously mentioned 9100F is dirt cheap, 9300/9320 for higher clockrate.
For all the Intel options would be ideal to wait for Comet Lake and enjoy the price drop or get the next-gen equivalent but I guess it can't be helped. They are at least worth considering though.
Won't get much out of it on a 3600 but it's free so might as well. Not that difficult.
Yes, but if overclocking doubles the power consumption something is probably on fire. Pcpartpicker isn't that great outside of the USA and finding good PSUs at a decent price is always difficult even with price comparison sites. You might just have to check whatever shop(s) you end up buying from manually.