How about this?
R5 2600, B450 board & RX580 8GB for $711.94 before rebates. $709 after shipping and rebates.
SG13 case for the most compact computer you could ever want, there is room to grow into an off the shelf water cooling later down the road. But a case is going to be 100% personal preference and you should pick what you like the most there.
Some of my thoughts about building budget PC's.
Keep your old systems whole and SELL THEM to help cover the cost of your new systems. If you steal this and that you will have a bunch of spare parts that no one wants. I kept my old Intel 2500K system whole and sold it plug and play ready to go for a whole lot more than I would have if i parted it out.
When you want to get the most for your money, don't buy fancy things like water cooling and instead shift those funds into the core components that will last you longer. You can always get things like water cooling later.
RX580 over the 1050ti because its faster and freesync later down the road. Nvidia also had driver issues that gave poor performance when mixed with Ryzen. Not sure if that has been fixed.
I have the SG13 case and R7 1700, my system is all air cooled and its dead silent except for when my video card fans rams up which is rare.
You can also drop some of the core components to what you have listed in your last pcpartpicker to save some money.
The other thing I noticed is that you have no HDD or OS on your PCPartPicker build, will you need those things?
Here is a complete system I dropped the RX580 down to a RX570 and added a 480Gb SSD, $706 before rebates. $698 after shipping and rebates.
If you want to save even more do what I did. Call the staples 1-800 number and have them price match this R5 1600 at micro center, I was able to get my R7 1700 for $203 back in 2017. The local stores refused to price match, I called the 1-800 number and had it purchased 5 mins later.