I see your point, I really don’t like leaving my old pc parts laying around collecting dust either, what I do is take my previous pc parts, put it together as Budget Builds then dump them off to Family and Friends whom do not know how to build pc’s, works like a charm :P Seriously, I do usually give it to them for Free though.
To better answer your question:
Your i5-3470 is a 10+ year old platform using only DDR “3” Ram, that platform is getting too old to bother with.
I looked into Bottleneck, that 660 Ti is already to weak for that 3470, So…
A couple comments I’ve seen in this Thread could help you to not have to throw it all way.

1. That 660 Ti is pretty much too old, but that 3470 can still effectively run a 1650, replace 660 TI w/ 1650.
2. SSD, If you’ve never owned an SSD you will be super impressed in how much faster that alone will make your PC, a whole lot, even with nothing else upgraded. You will have to re-install Windows onto that new SSD. A 2.5" 1TB SSD for about $40 on Amazon would do fine.

How about this, ran across it a few minutes ago so started a post with it in r/buildapcsales
https://www.reddit.com/r/buildapcsales/comments/186kl8l/cpuintel_core_i512600kf_core_i5_12th_gen_alder/
Your present MB may already have the needed Bios for that, double check on the Gigabyte website

https://www.reddit.com/r/buildapcsales/comments/18693hd/prebuilt_msi_codex_r_gaming_desktop_intel/
How about something like this. On Amazon the 13400f is $200, the 4060 8GB is $300, that is a decently priced Prebuilt.

Your 12100f & 6600 Complement each other, upgrading one of them will just cause the other to be a Bottleneck. I’d save the money for a complete overhaul.
A 13400, 13500 would allow you to keep your MB & Ram, that 12600k would work on your MB as well, you just wouldn’t be able to OC that K. The 13600k might be a bit much for your B660 due to Heat Issues.
pc-builds.com lists that 12600k as a Bottleneck for a 4070 at 1080p, I’m not sure If I believe that or not, I’m guessing that pair would be fine for Gaming, possibly not professional type work.
Comparing a 4070 to that 4060Ti, you’ll more than likely kick yourself after buying that 4060Ti, the 4070 is a good bit better, albeit more expensive as well.

A 13400 or 13500 would be a large upgrade to that i3 of yours, and you could stay with your present Motherboard and Ram, you would more than likely need to Flash to a newer Bios though.
What Video Card do you have though?
If your CPU isn’t the Bottleneck upgrading the Cpu wont help much.