Where can I look for USB 3.x superspeed mux chips for poor people that only have through-hole soldering tools?
I have never seen any USB chips that ever supported DIP packaged parts; not even in the original USB 1.0 era. Generally, support for new DIP parts industry-wide pretty much ended around the late 1990's. I assume the reason you're asking about through-hole is for ease of prototyping, but the world has moved on. All the good stuff is surface-mount now.

The USB Implementers Forum usb.org has all the specifications that go along with the "Designed for USB 3.1" branding. Basically if the device says designed for USB x.x, that means the designers read the USB spec and met all of the requirements.

The USB interface is very particular about maintaining signal integrity, trace impedance, and route matching between the matched pairs. Any USB design is going to require a specific PCB just for that design.

For hand-assembled prototyping, the key difference between surface-mount packages is whether or not the contacts are exposed.

"Friendly" packages such as SO (Small Outline), SSOP (Shrink Small Outline Package), TQFP (Thin Quad Flat Pack) connect to the PCB through small metal protrusions. These can be soldered in the usual way using a soldering iron to contact the pins and the PCB pads. You will need a stand magnifier or +10x glasses, steady hands, fine solder, good quality electronic soldering iron, and soldering flux.

"Unfriendly" packages such as TQFN (Thin Quad Flat Nightmare?), BGA (Ball Grid Array), CSP (Chip Scale Package), or WSP (Wafer Scale Package) connect to the PCB through metal contacts on the underside of the package. In the case of BGA/CSP/WSP these connections are completely hidden from view. Professional electronics technicians use flux and a temperature-controlled hot plate or temperature-controlled hot air wand (not a "heat gun" paint stripper, those will destroy the PCB). These packages are popular with OEM customers such as cellphone manufacturers, due to their extremely high circuit density. But they are really a pain to work with.

These related QA are a good resource: 

What tools, equipment, and techniques do you use to solder fine-pitch SMT parts?

How to hold SMD parts in place while soldering?